2016
3
2
2
0
Derivations of UPalgebras by means of UPendomorphisms
2
2
The notion of $f$derivations of UPalgebras 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 UPsubalgebras of UPalgebras,and also give examples to show that the two sets are not UPideals of UPalgebras in general.
1

1
20


Aiyared
Iampan
University of Phayao, Thailand
University of Phayao, Thailand
Thailand
aiyared.ia@up.ac.th
UPalgebra
UPsubalgebra
UPideal
$f$derivation
[[1] H. A. S. Abujabal, N. O. Alshehri, Some results on derivations of BCIalgebras, J. Nat. Sci. Math. 46##(no. 1&2) (2006), 13–19.##[2] H. A. S. Abujabal, N. O. Alshehri, On left derivations of BCIalgebras, Soochow J. Math. 33 (no. 3) (2007),##435–444.##[3] A. M. Alroqi, On generalized (α,β)derivations in BCIalgebras, J. Appl. Math. Inform. 32 (no. 1–2) (2014), 27–38.##[4] N. O. Alshehri, S. M. Bawazeer, On derivations of BCCalgebras, Int. J. Algebra 6 (no. 32) (2012), 1491–##[5] L. K. Ardekani, B. Davvaz, On generalized derivations of BCIalgebras and their properties, J. Math. 2014##(2014), Article ID 207161, 10 pages.##[6] S. M. Bawazeer, N. O. Alshehri, R. S. Babusail, Generalized derivations of BCCalgebras, Int. J. Math.##Math. Sci. 2013 (2013), Article ID 451212, 4 pages.##[7] Q. P. Hu, X. Li, On BCHalgebras, Math. Semin. Notes, Kobe Univ. 11 (1983), 313–320.##[8] A. Iampan, A new branch of the logical algebra: UPalgebras, Manuscript submitted for publication, April##[9] Y. Imai, K. Is´ eki, On axiom system of propositional calculi, XIV, Proc. Japan Acad. 42 (no. 1) (1966),##19–22.##[10] K. Is´ eki, An algebra related with a propositional calculus, Proc. Japan Acad. 42 (no. 1) (1966), 26–29.##[11] M. A. Javed, M. Aslam, A note on fderivations of BCIalgebras, Commun. Korean Math. Soc. 24 (no. 3)##(2009), 321–331.##[12] Y. B. Jun, X. L. Xin, On derivations of BCIalgebras, Inform. Sci. 159 (2004), 167–176.##[13] S. Keawrahun, U. Leerawat, On isomorphisms of SUalgebras, Sci. Magna 7 (no. 2) (2011), 39–44.##[14] K. J. Lee, A new kind of derivation in BCIalgebras, Appl. Math. Sci. 7 (no. 84) (2013), 4185–4194.##[15] P. H. Lee, T. K. Lee, On derivations of prime rings, Chinese J. Math. 9 (1981), 107–110.##[16] S. M. Lee, K. H. Kim, A note on fderivations of BCCalgebras, Pure Math. Sci. 1 (no. 2) (2012), 87–93.##[17] G. Muhiuddin, A. M. Alroqi, On (α,β)derivations in BCIalgebras, Discrete Dyn. Nat. Soc. 2012 (2012),##Article ID 403209, 11 pages.##[18] G. Muhiuddin, A. M. Alroqi, On tderivations of BCIalgebras, Abstr. Appl. Anal. 2012 (2012), Article##ID 872784, 12 pages.##[19] G. Muhiuddin, A. M. Alroqi, On generalized left derivations in BCIalgebras, Appl. Math. Inf. Sci. 8##(no. 3) (2014), 1153–1158.##[20] G. Muhiuddin, A. M. Alroqi, Y. B. Jun, Y. Ceven, On symmetric left biderivations in BCIalgebras, Int.##J. Math. Math. Sci. 2013 (2013), Article ID 238490, 6 pages.##[21] F. Nisar, Characterization of fderivations of a BCIalgebra, East Asian Math. J. 25 (no. 1) (2009), 69–87.##[22] F. Nisar, On Fderivations of BCIalgebras, J. Prime Res. Math. 5 (2009), 176–191.##[23] E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100.##[24] C. Prabpayak, U. Leerawat, On derivation of BCCalgebras, Kasetsart J. (Nat. Sci.) 43 (2009), 398–401.##[25] C. Prabpayak, U. Leerawat, On ideals and congruences in KUalgebras, Sci. Magna 5 (no. 1) (2009), 54–57.##[26] K. Sawika, R. Intasan, A. Kaewwasri, A. Iampan, Derivations of UPalgebras, Korean J. Math. 24 (no. 3)##(2016), 345–367.##[27] J. Zhan, Y. L. Liu, On fderivations of BCIalgebras, Int. J. Math. Math. Sci. 2005 (2005), 1675–1684.##]
A Note on Artinian Primes and Second Modules
2
2
Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.
1

21
29


Ahmad
Khaksari
Department of Mathematics, Payame Noor University, Tehran, Iran
Department of Mathematics, Payame Noor University,
Iran
a_khaksari@pnu.ac.ir
prime submodule
Second submodule
Injective and flat module
Catenary modules
Dimension of modules
[[1] F. Anderson and K. Fuller, Rings and categories of modules, Graduate Text in Mathematics, Springer##Verlag, Berlin New York, 1974.##[2] A. Azizi and H. Sharif, On Prime Submodules, Honam, Mathematical Journal, 21(1) (1999), 112##[3] M. F. Atiyah, I. G. Macdonald, Introduction to Commutative Algebra. AddisionWesley Publishing Com##pany, Inc, 1969.##[4] J. Dauns, Prime Modules, J. Reine angew Math 298 (1978), 156181.##[5] E. H. Feller and E. W. Swokowski, Prime Modules, Canad. J. Math. 17 (1965), 10411052.##[6] T. W. Hungerford, Algebra, SpringerVerlog, New York Inc, 1989.##[7] C. P. Lu, Prime Submodules of Modules, Comm. Math. Univ. Sancti. Pauli, 33 (1984), 6169##[8] C. P. Lu, Spectra of modules, CommAlgebra, 23 (10), (1995), 37413752.##[9] R. L. Mccaslad and M. E. Moore, Prime Submodules, Comm. Algebra, 20 (6) (1992), 18031817.##[10] H. Matsumura, Commutative Ring Theory, Cambridge University Press, Cambridge, 1992.##[11] S. Namazi and Y. Sharifi, Catenary Modules, Acta Math, Hungarica, 85 (3) (1999), 211218.##[12] R. Y. Sharp, A Method for the study of artinian modules, with an application to asymtotic behavior, math.##Sci. Res. Ins. Publ. 15 (1989), 443465,SpringerVerlag##[13] R. Y. Sharp, Steps in commutative Algebra, Cambridge University Press 1990.##[14] Y. Tiras and M. Alkan, Prime modules and submodules, Comm. Algebra, 31 (11) (2003), 52535261.##]
On some classes of expansions of ideals in $MV$algebras
2
2
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.
1

31
47


Fereshteh
Foruzesh
Faculty of Mathematics and computing, Higher Education Complex of Bam, Kerman, Iran.
Faculty of Mathematics and computing, Higher
Iran


Mahta
Bedrood
Department of Mathematics , Shahid Bahonar University
Kerman, Iran.
Department of Mathematics , Shahid Bahonar
Iran
bedrood.m@gmail.com
Expansion of an ideal
sigma)primary $
sigma)$obstinate
$ (tau
sigma)$Boolean
Heyting algebra
[[1] A. Filipoiu, G. Georgescu, A. Lettieri, Maximal MV algebras, Mathware, soft comput., 4 (1997), pp. 53–62.##[2] C. C. Chang, Algebraic analysis of many valued logic, Trans. Amer. Math. Soc., 88 (1958), pp. 467–490.##[3] C. C. Chang, A new proof of the completeness of the Lukasiewicz axioms,Trans. Amer. Math. Soc., 93##(1959), pp. 74–80.##[4] R. Cignoli, I. M. L. D’Ottaviano, D. Mundici, Algebraic foundations of many valued reasoning, Kluwer##Academic, Dordrecht, (2000).##[5] F. Forouzesh, E. Eslami, A. Borumand saeid, On obstinate ideals in MV −algebras, Politehn. Univ.##Bucharest Sci. Bull. Ser. A Appl. Math. Phys. Vol. 76, (2014), pp. 53–62.##[6] C. S. Hoo, S. Sessa, Implicative and Boolean ideals of MValgebras, Math. Japon. 39 (1994), pp. 215219.##[7] S. Motamed, J. Moghaderi, Expansions of filters in Residuated lattices, International Journal of Contem##porary Mathematical siences, Vol. 11 (2016), pp. 915.##[8] D. Piciu, Algebras of fuzzy logic, Ed. Universitaria Craiova (2007).##]
A new approach to characterization of MValgebras
2
2
By considering the notion of MValgebras, we recall some results on enumeration of MValgebras and wecarry out a study on characterization of MValgebras of orders $2$, $3$, $4$, $5$, $6$ and $7$. We obtain that there is one nonisomorphic MValgebra of orders $2$, $3$, $5$ and $7$ and two nonisomorphic MValgebras of orders $4$ and $6$.
1

49
70


Saeed
Rasouli
Department of Mathematics, Persian Gulf University, Bushehr, 75169, Iran
Department of Mathematics, Persian Gulf University
Iran
saeedmath@yahoo.com
MValgebra
Lattice
distributive lattice
ideal
sub MValgebra
[[1] L. P. Belluce and A. Di Nola, Yosida type representation for perfect MValgebras, Math. Logic Quarterly,##Vol 42 (1996), pp. 551563.##[2] S. Burris and H. P. Sankappanavar, A course in universal algebra, Graduate Text in Mathematics, Vol. 78,##SpringerVerlag, New York Heidelberg Berlin, (1981).##[3] C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. Vol 88 (1958), pp. 467490.##[4] C. C. Chang, A new proof of the completeness of the Lukasiewicz axioms, Trans. Amer. Math. Soc. Vol 93##No. 1 (1959), pp. 7480.##[5] R. Cignoli, I. D’Ottaviano and D. Mundici, Algebras das logicas the Lukasiewics, 1st ed., Centro de Logica,##Epistemologia e Historia da Ciencia, Campinas, Brazil, (1994).##[6] L. C. Ciungu, Directly indecomposable residuated lattices, Iranian journal of fuzzy systems Vol. 6 No. 2##(2009), pp. 718.##[7] A. Di Nola, One chain generated varieties of MValgebras, J. of algebra, Vol. 225 (2000), pp. 667697.##[8] A. Di Nola, R. Grigolia and A. Lettieri, Projective MValgebras, Internat. J. Approx. Reason. Vol. 47##(2008), pp. 323332.##[9] A. Filipoiu, G. Georgescu and A. Lettieri, Maximal MValgebras, Mathware and soft computing, Vl. 4##(1997), pp. 5362.##[10] G. Gratzer, Lattice theory First concepts and distributive lattices, W. H. Freeman and Co., San Francisco,##Calif., (1971).##[11] J. Jakubik, Direct product decompositions of MValgebras, Czech. Math. J. 44 (1994) 725739.##[12] J. Jakubik, Direct product decompositions of pseudo MValgebras, Archivum Math. Vol. 37 (2001), pp.##[13] W. Komori, SuperLukasiewicz propositional logics, Nagoya Math. J. Vol. 84 (1981), pp. 119133.##[14] D. Mundici, Interpretation of AFC*algebras in Lukasiewicz sentential calculus, J. Funct. Anal. Vol. 65##(1986), pp. 1563.##[15] S. Rasouli, B. Davvaz, Roughness in MValgebras, Information Sciences, Vol. 180, No. 5 (2010), pp. 737747.##[16] S. Rasouli, B. Davvaz, Homomorphism, Ideals and Binary Relations on HyperMV Algebras, Multiple##valued Logic and Soft Computing, Vol. 17, No. 1 (2011), pp. 4768.##[17] B. Teheux, Lattice of subalgebras in the finitely generated varieties of MValgebras, Discrete Mathematics, Vol. 307 (2007), pp. 22612275.##[18] E. Turunen, Mathematics behind fuzzy logic. PhysicaVerlag, Heidelberg, (1999).##]
The remoteness of the permutation code of the group $U_{6n}$
2
2
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 $2n+2$.
1

71
79


Masoomeh
YazdaniMoghaddam
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
Department of Pure Mathematics, Faculty of
Iran
m.yazdani.m@grad.kashanu.ac.ir


Reza
Kahkeshani
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
Department of Pure Mathematics, Faculty of
Iran
kahkeshanireza@kashanu.ac.ir
permutation code
permutation array
remoteness
group $U_{6n}$
[[1] R.F. Bailey, Errorcorrecting codes from the permutation groups, Discrete Math .30 9(2009) 42534265.##[2] P.J. Cameron, Permutation codes, Eur. J. Combin. 31 (2010) 482490.##[3] P.J. Cameron, M. Gadouleau, Remoteness of permutation codes, Eur. J. Combin. 33 (2012) 12731285.##[4] P.J. Cameron, .IM. Wanless Covering radius for set of permutations, Discrete Math. 293 (2005) 91109.##[5] W. Chu W, C.J. Colbourn, P. Duke, P. Construction for code in powerline communications, Design code ryptogr. 32 (2004) 5164.##[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) 117.##[7] H. Farahat, The symmetric group as a metric space, .J London Math. Soc. 35 (1960) 215220.##[8] F.J. MacWilliams, N.J.A. Sloan, The Theory of ErrorCorrecting Codes, Amsterdam, Netherlands: NorthHolland Publishing Co.,(1977).##]
The distinguishing chromatic number of bipartite graphs of girth at least six
2
2
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.
1

81
87


Saeid
Alikhani
Department Mathematics, Yazd University
89195741, Yazd, Iran
Department Mathematics, Yazd University
89195741,
Iran
alikhani@yazd.ac.ir


Samaneh
Soltani
Department Mathematics, Yazd University
89195741, Yazd, Iran
Department Mathematics, Yazd University
89195741,
Iran
s.soltani1979@gmail.com
distinguishing number
distinguishing chromatic number
symmetry breaking
[[1] M.O. Albertson and K.L. Collins, Symmetry breaking in graphs, Electron. J. Combin. 3 (1996), #R18.##[2] K.L. Collins and A.N. Trenk, The distinguishing chromatic number, Electron. J. Combin. 13 (1) (2006),##[3] D.W. Cranston, Proper distinguishing colorings with few colors for graphs with girth at least 5. arXiv##preprint arXiv:1707.05439##[4] J. Gross and J. Yellen, Handbook of Graph Theory, CRC Press, Boca Raton, 2004.##[5] C. Laflamme and K. Seyffarth, Distinguishing chromatic numbers of bipartite graphs, Electron. J. Combin.##16 (1) (2009), #R76.##]