Derivations of UP-algebras by means of UP-endomorphisms
Aiyared
Iampan
University of Phayao
author
text
article
2017
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
3
v.
2
no.
2017
1
20
http://as.yazd.ac.ir/article_901_f422878003a1475eef8b5d834bc3679e.pdf
A Note on Artinian Primes and Second Modules
Ahmad
Khaksari
Department of Mathematics, Payame Noor University, Tehran, Iran
author
text
article
2016
eng
Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.
Algebraic Structures and Their Applications
Yazd University
2382-9761
3
v.
2
no.
2016
21
29
http://as.yazd.ac.ir/article_953_b2552b7859f51a9b570e841a3799b41d.pdf
On some classes of expansions of ideals in $MV$-algebras
Fereshteh
Foruzesh
Faculty of Mathematics and computing, Higher Education Complex of Bam, Kerman, Iran.
author
Mahta
Bedrood
Department of Mathematics , Shahid Bahonar University
Kerman, Iran.
author
text
article
2016
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
3
v.
2
no.
2016
31
47
http://as.yazd.ac.ir/article_954_72d43e9972d37dc2a7361805371f5338.pdf
A new approach to characterization of MV-algebras
Saeed
Rasouli
Department of Mathematics, Persian Gulf University, Bushehr, 75169, Iran
author
text
article
2016
eng
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 $6$.
Algebraic Structures and Their Applications
Yazd University
2382-9761
3
v.
2
no.
2016
49
70
http://as.yazd.ac.ir/article_955_0a544bda63302897572bdf6c822b878b.pdf
The remoteness of the permutation code of the group $U_{6n}$
Masoomeh
Yazdani-Moghaddam
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
author
Reza
Kahkeshani
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
author
text
article
2017
eng
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 $2n+2$.
Algebraic Structures and Their Applications
Yazd University
2382-9761
3
v.
2
no.
2017
71
79
http://as.yazd.ac.ir/article_1057_e952e1a0228926a551882b8da6e21c01.pdf
The distinguishing chromatic number of bipartite graphs of girth at least six
Saeid
Alikhani
Department Mathematics, Yazd University
89195-741, Yazd, Iran
author
Samaneh
Soltani
Department Mathematics, Yazd University
89195-741, Yazd, Iran
author
text
article
2016
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
3
v.
2
no.
2016
81
87
http://as.yazd.ac.ir/article_1061_d7a2c4d97e197bfadafec3fd409da617.pdf