ORIGINAL_ARTICLE
Derivations of UP-algebras by means of UP-endomorphisms
The notion of $f$-derivations of UP-algebras is introduced, some useful examples are discussed, and related properties are investigated. Moreover, we show that the fixed set and the kernel of $f$-derivations are UP-subalgebras of UP-algebras,and also give examples to show that the two sets are not UP-ideals of UP-algebras in general.
http://as.yazd.ac.ir/article_901_f422878003a1475eef8b5d834bc3679e.pdf
2017-04-20T11:23:20
2018-12-19T11:23:20
1
20
UP-algebra
UP-subalgebra
UP-ideal
$f$-derivation
Aiyared
Iampan
aiyared.ia@up.ac.th
true
1
University of Phayao, Thailand
University of Phayao, Thailand
University of Phayao, Thailand
LEAD_AUTHOR
[1] H. A. S. Abujabal, N. O. Al-shehri, Some results on derivations of BCI-algebras, J. Nat. Sci. Math. 46
1
(no. 1&2) (2006), 13–19.
2
[2] H. A. S. Abujabal, N. O. Al-shehri, On left derivations of BCI-algebras, Soochow J. Math. 33 (no. 3) (2007),
3
435–444.
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[3] A. M. Al-roqi, On generalized (α,β)-derivations in BCI-algebras, J. Appl. Math. Inform. 32 (no. 1–2) (2014), 27–38.
5
[4] N. O. Al-shehri, S. M. Bawazeer, On derivations of BCC-algebras, Int. J. Algebra 6 (no. 32) (2012), 1491–
6
[5] L. K. Ardekani, B. Davvaz, On generalized derivations of BCI-algebras and their properties, J. Math. 2014
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(2014), Article ID 207161, 10 pages.
8
[6] S. M. Bawazeer, N. O. Alshehri, R. S. Babusail, Generalized derivations of BCC-algebras, Int. J. Math.
9
Math. Sci. 2013 (2013), Article ID 451212, 4 pages.
10
[7] Q. P. Hu, X. Li, On BCH-algebras, Math. Semin. Notes, Kobe Univ. 11 (1983), 313–320.
11
[8] A. Iampan, A new branch of the logical algebra: UP-algebras, Manuscript submitted for publication, April
12
[9] Y. Imai, K. Is´ eki, On axiom system of propositional calculi, XIV, Proc. Japan Acad. 42 (no. 1) (1966),
13
19–22.
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[10] K. Is´ eki, An algebra related with a propositional calculus, Proc. Japan Acad. 42 (no. 1) (1966), 26–29.
15
[11] M. A. Javed, M. Aslam, A note on f-derivations of BCI-algebras, Commun. Korean Math. Soc. 24 (no. 3)
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(2009), 321–331.
17
[12] Y. B. Jun, X. L. Xin, On derivations of BCI-algebras, Inform. Sci. 159 (2004), 167–176.
18
[13] S. Keawrahun, U. Leerawat, On isomorphisms of SU-algebras, Sci. Magna 7 (no. 2) (2011), 39–44.
19
[14] K. J. Lee, A new kind of derivation in BCI-algebras, Appl. Math. Sci. 7 (no. 84) (2013), 4185–4194.
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[15] P. H. Lee, T. K. Lee, On derivations of prime rings, Chinese J. Math. 9 (1981), 107–110.
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[16] S. M. Lee, K. H. Kim, A note on f-derivations of BCC-algebras, Pure Math. Sci. 1 (no. 2) (2012), 87–93.
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[17] G. Muhiuddin, A. M. Al-roqi, On (α,β)-derivations in BCI-algebras, Discrete Dyn. Nat. Soc. 2012 (2012),
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Article ID 403209, 11 pages.
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[18] G. Muhiuddin, A. M. Al-roqi, On t-derivations of BCI-algebras, Abstr. Appl. Anal. 2012 (2012), Article
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ID 872784, 12 pages.
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[19] G. Muhiuddin, A. M. Al-roqi, On generalized left derivations in BCI-algebras, Appl. Math. Inf. Sci. 8
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(no. 3) (2014), 1153–1158.
28
[20] G. Muhiuddin, A. M. Al-roqi, Y. B. Jun, Y. Ceven, On symmetric left bi-derivations in BCI-algebras, Int.
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J. Math. Math. Sci. 2013 (2013), Article ID 238490, 6 pages.
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[21] F. Nisar, Characterization of f-derivations of a BCI-algebra, East Asian Math. J. 25 (no. 1) (2009), 69–87.
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[22] F. Nisar, On F-derivations of BCI-algebras, J. Prime Res. Math. 5 (2009), 176–191.
32
[23] E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100.
33
[24] C. Prabpayak, U. Leerawat, On derivation of BCC-algebras, Kasetsart J. (Nat. Sci.) 43 (2009), 398–401.
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[25] C. Prabpayak, U. Leerawat, On ideals and congruences in KU-algebras, Sci. Magna 5 (no. 1) (2009), 54–57.
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[26] K. Sawika, R. Intasan, A. Kaewwasri, A. Iampan, Derivations of UP-algebras, Korean J. Math. 24 (no. 3)
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(2016), 345–367.
37
[27] J. Zhan, Y. L. Liu, On f-derivations of BCI-algebras, Int. J. Math. Math. Sci. 2005 (2005), 1675–1684.
38
ORIGINAL_ARTICLE
A Note on Artinian Primes and Second Modules
Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.
http://as.yazd.ac.ir/article_953_b2552b7859f51a9b570e841a3799b41d.pdf
2016-04-01T11:23:20
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21
29
prime submodule
Second submodule
Injective and flat module
Catenary modules
Dimension of modules
Ahmad
Khaksari
a_khaksari@pnu.ac.ir
true
1
Department of Mathematics, Payame Noor University, Tehran, Iran
Department of Mathematics, Payame Noor University, Tehran, Iran
Department of Mathematics, Payame Noor University, Tehran, Iran
LEAD_AUTHOR
[1] F. Anderson and K. Fuller, Rings and categories of modules, Graduate Text in Mathematics, Springer-
1
Verlag, Berlin- New York, 1974.
2
[2] A. Azizi and H. Sharif, On Prime Submodules, Honam, Mathematical Journal, 21(1) (1999), 1-12
3
[3] M. F. Atiyah, I. G. Macdonald, Introduction to Commutative Algebra. Addision-Wesley Publishing Com-
4
pany, Inc, 1969.
5
[4] J. Dauns, Prime Modules, J. Reine angew Math 298 (1978), 156-181.
6
[5] E. H. Feller and E. W. Swokowski, Prime Modules, Canad. J. Math. 17 (1965), 1041-1052.
7
[6] T. W. Hungerford, Algebra, Springer-Verlog, New York Inc, 1989.
8
[7] C. P. Lu, Prime Submodules of Modules, Comm. Math. Univ. Sancti. Pauli, 33 (1984), 61-69
9
[8] C. P. Lu, Spectra of modules, Comm-Algebra, 23 (10), (1995), 3741-3752.
10
[9] R. L. Mccaslad and M. E. Moore, Prime Submodules, Comm. Algebra, 20 (6) (1992), 1803-1817.
11
[10] H. Matsumura, Commutative Ring Theory, Cambridge University Press, Cambridge, 1992.
12
[11] S. Namazi and Y. Sharifi, Catenary Modules, Acta Math, Hungarica, 85 (3) (1999), 211-218.
13
[12] R. Y. Sharp, A Method for the study of artinian modules, with an application to asymtotic behavior, math.
14
Sci. Res. Ins. Publ. 15 (1989), 443-465,Springer-Verlag
15
[13] R. Y. Sharp, Steps in commutative Algebra, Cambridge University Press 1990.
16
[14] Y. Tiras and M. Alkan, Prime modules and submodules, Comm. Algebra, 31 (11) (2003), 5253-5261.
17
ORIGINAL_ARTICLE
On some classes of expansions of ideals in $MV$-algebras
In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (\tau,\sigma)- $primary, $ (\tau,\sigma)$-obstinate and $ (\tau,\sigma)$-Boolean in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (\tau,\sigma)$-obstinate ideal of an $ MV-$ algebra is $ (\tau,\sigma)$-primary and $ (\tau,\sigma)$-Boolean. In particular, we define an expansion $ \sigma_{y} $ of ideals in an $ MV-$algebra. A characterization of expansion ideal with respect to $ \sigma_{y} $ is given. Finally, we show that the class $ C(\sigma_{y}) $ of all constant ideals relative to $ \sigma_{y} $ is a Heyting algebra.
http://as.yazd.ac.ir/article_954_72d43e9972d37dc2a7361805371f5338.pdf
2016-04-01T11:23:20
2018-12-19T11:23:20
31
47
Expansion of an ideal
sigma)-primary $
sigma)$-obstinate
$ (tau
sigma)$-Boolean
Heyting algebra
Fereshteh
Foruzesh
true
1
Faculty of Mathematics and computing, Higher Education Complex of Bam, Kerman, Iran.
Faculty of Mathematics and computing, Higher Education Complex of Bam, Kerman, Iran.
Faculty of Mathematics and computing, Higher Education Complex of Bam, Kerman, Iran.
LEAD_AUTHOR
Mahta
Bedrood
bedrood.m@gmail.com
true
2
Department of Mathematics , Shahid Bahonar University
Kerman, Iran.
Department of Mathematics , Shahid Bahonar University
Kerman, Iran.
Department of Mathematics , Shahid Bahonar University
Kerman, Iran.
AUTHOR
[1] A. Filipoiu, G. Georgescu, A. Lettieri, Maximal MV -algebras, Mathware, soft comput., 4 (1997), pp. 53–62.
1
[2] C. C. Chang, Algebraic analysis of many valued logic, Trans. Amer. Math. Soc., 88 (1958), pp. 467–490.
2
[3] C. C. Chang, A new proof of the completeness of the Lukasiewicz axioms,Trans. Amer. Math. Soc., 93
3
(1959), pp. 74–80.
4
[4] R. Cignoli, I. M. L. D’Ottaviano, D. Mundici, Algebraic foundations of many valued reasoning, Kluwer
5
Academic, Dordrecht, (2000).
6
[5] F. Forouzesh, E. Eslami, A. Borumand saeid, On obstinate ideals in MV −algebras, Politehn. Univ.
7
Bucharest Sci. Bull. Ser. A Appl. Math. Phys. Vol. 76, (2014), pp. 53–62.
8
[6] C. S. Hoo, S. Sessa, Implicative and Boolean ideals of MV-algebras, Math. Japon. 39 (1994), pp. 215-219.
9
[7] S. Motamed, J. Moghaderi, Expansions of filters in Residuated lattices, International Journal of Contem-
10
porary Mathematical siences, Vol. 11 (2016), pp. 9-15.
11
[8] D. Piciu, Algebras of fuzzy logic, Ed. Universitaria Craiova (2007).
12
ORIGINAL_ARTICLE
A new approach to characterization of MV-algebras
By considering the notion of MV-algebras, we recall some results on enumeration of MV-algebras and wecarry out a study on characterization of MV-algebras of orders $2$, $3$, $4$, $5$, $6$ and $7$. We obtain that there is one non-isomorphic MV-algebra of orders $2$, $3$, $5$ and $7$ and two non-isomorphic MV-algebras of orders $4$ and $6$.
http://as.yazd.ac.ir/article_955_0a544bda63302897572bdf6c822b878b.pdf
2016-04-01T11:23:20
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49
70
MV-algebra
Lattice
distributive lattice
ideal
sub MV-algebra
Saeed
Rasouli
saeedmath@yahoo.com
true
1
Department of Mathematics, Persian Gulf University, Bushehr, 75169, Iran
Department of Mathematics, Persian Gulf University, Bushehr, 75169, Iran
Department of Mathematics, Persian Gulf University, Bushehr, 75169, Iran
LEAD_AUTHOR
[1] L. P. Belluce and A. Di Nola, Yosida type representation for perfect MV-algebras, Math. Logic Quarterly,
1
Vol 42 (1996), pp. 551-563.
2
[2] S. Burris and H. P. Sankappanavar, A course in universal algebra, Graduate Text in Mathematics, Vol. 78,
3
Springer-Verlag, New York Heidelberg Berlin, (1981).
4
[3] C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. Vol 88 (1958), pp. 467-490.
5
[4] C. C. Chang, A new proof of the completeness of the Lukasiewicz axioms, Trans. Amer. Math. Soc. Vol 93
6
No. 1 (1959), pp. 74-80.
7
[5] R. Cignoli, I. D’Ottaviano and D. Mundici, Algebras das logicas the Lukasiewics, 1st ed., Centro de Logica,
8
Epistemologia e Historia da Ciencia, Campinas, Brazil, (1994).
9
[6] L. C. Ciungu, Directly indecomposable residuated lattices, Iranian journal of fuzzy systems Vol. 6 No. 2
10
(2009), pp. 7-18.
11
[7] A. Di Nola, One chain generated varieties of MV-algebras, J. of algebra, Vol. 225 (2000), pp. 667-697.
12
[8] A. Di Nola, R. Grigolia and A. Lettieri, Projective MV-algebras, Internat. J. Approx. Reason. Vol. 47
13
(2008), pp. 323-332.
14
[9] A. Filipoiu, G. Georgescu and A. Lettieri, Maximal MV-algebras, Mathware and soft computing, Vl. 4
15
(1997), pp. 53-62.
16
[10] G. Gratzer, Lattice theory First concepts and distributive lattices, W. H. Freeman and Co., San Francisco,
17
Calif., (1971).
18
[11] J. Jakubik, Direct product decompositions of MV-algebras, Czech. Math. J. 44 (1994) 725-739.
19
[12] J. Jakubik, Direct product decompositions of pseudo MV-algebras, Archivum Math. Vol. 37 (2001), pp.
20
[13] W. Komori, Super-Lukasiewicz propositional logics, Nagoya Math. J. Vol. 84 (1981), pp. 119-133.
21
[14] D. Mundici, Interpretation of AFC*-algebras in Lukasiewicz sentential calculus, J. Funct. Anal. Vol. 65
22
(1986), pp. 15-63.
23
[15] S. Rasouli, B. Davvaz, Roughness in MV-algebras, Information Sciences, Vol. 180, No. 5 (2010), pp. 737-747.
24
[16] S. Rasouli, B. Davvaz, Homomorphism, Ideals and Binary Relations on Hyper-MV Algebras, Multiple-
25
valued Logic and Soft Computing, Vol. 17, No. 1 (2011), pp. 47-68.
26
[17] B. Teheux, Lattice of subalgebras in the finitely generated varieties of MV-algebras, Discrete Mathematics, Vol. 307 (2007), pp. 2261-2275.
27
[18] E. Turunen, Mathematics behind fuzzy logic. Physica-Verlag, Heidelberg, (1999).
28
ORIGINAL_ARTICLE
The remoteness of the permutation code of the group $U_{6n}$
Recently, a new parameter of a code, referred to as the remoteness, has been introduced.This parameter can be viewed as a dual to the covering radius. It is exactly determined for the cyclic and dihedral groups. In this paper, we consider the group $U_{6n}$ as a subgroup of $S_{2n+3}$ and obtain its remoteness. We show that the remoteness of the permutation code $U_{6n}$ is $2n+2$. Moreover, it is proved that the covering radius of $U_{6n}$ is also $2n+2$.
http://as.yazd.ac.ir/article_1057_758aa9213fb349f92e6a2c3f83d75f99.pdf
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71
79
permutation code
permutation array
remoteness
group $U_{6n}$
Masoomeh
Yazdani-Moghaddam
m.yazdani.m@grad.kashanu.ac.ir
true
1
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
AUTHOR
Reza
Kahkeshani
kahkeshanireza@kashanu.ac.ir
true
2
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
LEAD_AUTHOR
[1] R.F. Bailey, Error-correcting codes from the permutation groups, Discrete Math .30 9(2009) 4253-4265.
1
[2] P.J. Cameron, Permutation codes, Eur. J. Combin. 31 (2010) 482-490.
2
[3] P.J. Cameron, M. Gadouleau, Remoteness of permutation codes, Eur. J. Combin. 33 (2012) 1273-1285.
3
[4] P.J. Cameron, .IM. Wanless Covering radius for set of permutations, Discrete Math. 293 (2005) 91-109.
4
[5] W. Chu W, C.J. Colbourn, P. Duke, P. Construction for code in powerline communications, Design code ryptogr. 32 (2004) 51-64.
5
[6] M.R. Darafsheh, N.S. Poursalavati, On the existence of the orthogonal basis of the symmetry classes of tensors associated with certain groups, Sut. J. Math. 37 (2001) 1-17.
6
[7] H. Farahat, The symmetric group as a metric space, .J London Math. Soc. 35 (1960) 215-220.
7
[8] F.J. MacWilliams, N.J.A. Sloan, The Theory of Error-Correcting Codes, Amsterdam, Netherlands: North-Holland Publishing Co.,(1977).
8
ORIGINAL_ARTICLE
The distinguishing chromatic number of bipartite graphs of girth at least six
The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The distinguishing chromatic number $\chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum degree $\Delta (G)$, then $\chi_{D}(G)\leq \Delta (G)+1$. We also obtain an upper bound for $\chi_{D}(G)$ where $G$ is a graph with at most one cycle. Finally, we state a relationship between the distinguishing chromatic number of a graph and its spanning subgraphs.
http://as.yazd.ac.ir/article_1061_d7a2c4d97e197bfadafec3fd409da617.pdf
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81
87
distinguishing number
distinguishing chromatic number
symmetry breaking
Saeid
Alikhani
alikhani@yazd.ac.ir
true
1
Department Mathematics, Yazd University
89195-741, Yazd, Iran
Department Mathematics, Yazd University
89195-741, Yazd, Iran
Department Mathematics, Yazd University
89195-741, Yazd, Iran
LEAD_AUTHOR
Samaneh
Soltani
s.soltani1979@gmail.com
true
2
Department Mathematics, Yazd University
89195-741, Yazd, Iran
Department Mathematics, Yazd University
89195-741, Yazd, Iran
Department Mathematics, Yazd University
89195-741, Yazd, Iran
AUTHOR
[1] M.O. Albertson and K.L. Collins, Symmetry breaking in graphs, Electron. J. Combin. 3 (1996), #R18.
1
[2] K.L. Collins and A.N. Trenk, The distinguishing chromatic number, Electron. J. Combin. 13 (1) (2006),
2
[3] D.W. Cranston, Proper distinguishing colorings with few colors for graphs with girth at least 5. arXiv
3
preprint arXiv:1707.05439
4
[4] J. Gross and J. Yellen, Handbook of Graph Theory, CRC Press, Boca Raton, 2004.
5
[5] C. Laflamme and K. Seyffarth, Distinguishing chromatic numbers of bipartite graphs, Electron. J. Combin.
6
16 (1) (2009), #R76.
7