Yazd UniversityAlgebraic Structures and Their Applications2382-97615120180201An investigation on regular relations of universal hyperalgebras121117110.22034/as.2018.1171ENS.RasouliDepartment of Mathematics,
Persian Gulf University,
Bushehr, 75169, IranB.DavvazDepartment of Mathematics
Yazd University
Yazd, IranJournal Article20170504In this paper, by considering the notion of $\Sigma$-hyperalgebras for an arbitrary signature $\Sigma$, we study the notions of regular and strongly regular relations on a $\Sigma$-hyperalgebra, $\mathfrak{A}$. We show that each regular relation which contains a strongly regular relation is a strongly regular relation. Then we concentrate on the connection between the fundamental relation of $\mathfrak{A}$ and the set of complete parts of $\mathfrak{A}$.https://as.yazd.ac.ir/article_1171_ee37ba41304093beaa74969ad5e9db30.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97615120180201An efficient algorithm for Mixed domination on Generalized Series-Parallel Graphs2339120810.22034/as.2018.1208ENM.RajaatiDepartment of Computer Science, Yazd University, Yazd, Iran.M.R.HooshmandaslDepartment of Computer Science, Yazd University, Yazd, Iran.A.ShakibaDepartment of Computer Science,
Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran.P.SharifaniDepartment of Computer Science,
Yazd University, Yazd, Iran.M.J.DinneenDepartment of Computer Science,
The University of Auckland,
Auckland, New Zealand.Journal Article20180420A mixed dominating set $S$ of a graph $G=(V, E)$ is a subset of vertices and edges like $S \subseteq V \cup E$ such that each element $v\in (V \cup E) \setminus S$ is adjacent or incident to at least one element in $S$. The mixed domination number $\gamma_m(G)$ of a graph $G$ is the minimum cardinality among all mixed dominating sets in $G$. The problem of finding $\gamma_{m}(G)$ is known to be NP-complete. In this paper, we present an explicit polynomial-time algorithm using the parse tree to construct a mixed dominating set of size $\gamma_{m}(G)$ where $G$ is a generalized series-parallel graph.https://as.yazd.ac.ir/article_1208_a3d01b0ef81b9ace16f3dc16a272884d.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97615120180201A short Note on prime submodules4149120910.22034/as.2018.1209ENJafarA'zamiDepartment of mathematics, Faculty of sciences, University of Mohaghegh Ardabili, Ardabil, Iran.Journal Article20171109Let $R$ be a commutative ring with identity and $M$ be a unital $R$-module. A proper submodule $N$ of $M$ with $N:_RM=\frak p$ is said to be prime or $\frak p$-prime ($\frak p$ a prime ideal of $R$) if $rx\in N$ for $r\in R$ and $x\in M$ implies that either $x\in N$ or $r\in \frak p$. In this paper we study a new equivalent conditions for a minimal prime submodules of an $R$-module to be a finite set, whenever $R$ is a Noetherian ring. Also we introduce the concept of arithmetic rank of a submodule of a Noetherian module and we give an upper bound for it.https://as.yazd.ac.ir/article_1209_0c73ba791d9609f1a9176263ae0fbd5b.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97615120180201Boolean center of lattice ordered $EQ$-algebras with bottom element5168121010.22034/as.2018.1210ENNedaMohtashamniaDepartement of Mathematics, Kerman Branch, Islamic Azad university, Kerman,Iran.LidaTorkzadehDepartement of Mathematics, Kerman Branch, Islamic Azad university, Kerman,Iran.Journal Article20171224In this paper, some new properties of $EQ$-algebras are investigated. We introduce and study the notion of Boolean center of lattice ordered $EQ$-algebras with bottom element. We show that in a good $\ell EQ$-algebra $E$ with bottom element the complement of an element is unique. Furthermore, Boolean elements of a good bounded lattice $EQ$-algebra are characterized. Finally, we obtain conditions under which Boolean center of an $EQ$-algebra $E$ is the subalgebra of $E$. https://as.yazd.ac.ir/article_1210_746371f11fda39097a765404e37a9111.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97615120180201On endo-semiprime and endo-cosemiprime modules6980121110.22034/as.2018.1211ENParvinKarimi BeiranvandDepartment of mathematics, Lorestan university,P.O.Box 465, Khoramabad, Iran.0000-0002-5584-6455RezaBeyranvandDepartment of mathematics, Lorestan university, P.O.Box 465, Khoramabad, Iran.Journal Article20180715In this paper, we study the notions of endo-semiprime and endo-cosemiprime modules and obtain some related results. For instance, we show that in a right self-injective ring $R$, all nonzero ideals of $R$ are endo-semiprime as right (left) $R$-modules if and only if $R$ is semiprime. Also, we prove that both being endo-semiprime and being are Morita invariant properties.https://as.yazd.ac.ir/article_1211_7708ce7a15d1e37878a47603f0c774c7.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97615120180201On dual of the generalized splitting matroids8188121310.22034/as.2018.1213ENGhodratGhafariDepartment of Mathematics, Urmia University, Urmia, Iran0000-0002-3695-9446GhodratollahAzadiDepartment of Mathematics, Urmia University, Urmia, Iran0000-0002-1807-4732HabibAzanchilerDepartment of Mathematics, Urmia University, Urmia, IranJournal Article20180521Given a binary matroid $M$ and a subset $T\subseteq E(M)$, Luis A. Goddyn posed a problem that the dual of the splitting of $M$, i.e., ($(M_{T})^{*}$) is not always equal to the splitting of the dual of $M$, ($(M^{*})_{T}$). This persuade us to ask if we can characterize those binary matroids for which $(M_{T})^{*}=(M^{*})_{T}$. Santosh B. Dhotre answered this question for a two-element subset $T$. In this paper, we generalize his result for any subset $T\subseteq E(M)$ and exhibit a criterion for a binary matroid $M$ and subsets $T$ for which $(M_{T})^{*}$ and $(M^{*})_{T}$ are the equal. We also show that there is no subset $T\subseteq E(M)$ for which, the dual of element splitting of $M$, i.e., ($(M^{'}_{T})^{*}$) equals to the element splitting of the dual of $M$, (($M^{*})^{'}_{T}$).https://as.yazd.ac.ir/article_1213_5cd3e29998682a9da665160814771b1c.pdf