University of GuilanJournal of Algebra and Related Topics2345-39319120210601P-Regular and P-Local Rings119480410.22124/jart.2021.17609.1230ENH. IbrahimHakmiDepartment of Mathematics
Faculty of Sciences
Damascus University, Syria0000-0002-4583-2009Journal Article20200909This paper is a continuation of study rings relative to right<br />ideal, where we study the concepts of regular and local rings<br />relative to right ideal. We give some relations between $P-$local<br />($P-$regular) and local (regular) rings. New characterization<br />obtained include necessary and sufficient conditions of a ring $R$<br />to be regular, local ring in terms $P-$regular, $P-$local of<br />matrices ring $M_{2}(R)$. Also, We proved that every ring is local<br />relative to any maximal right ideal of it.University of GuilanJournal of Algebra and Related Topics2345-39319120210601Some classes of perfect annihilator-ideal graphs associated with commutative rings2129480510.22124/jart.2021.17227.1214ENM.AdlifardDepartment of Mathematics, Roudbar Branch Islamic Azad University, Roudbar, IranSh.PayroviDepartment of Mathematics, Imam Khomeini International University, Qazvin, IranJournal Article20200727Let $R$ be a commutative ring and let $\Bbb A(R)$ be<br />the set of all ideals of $R$ with nonzero annihilator.<br />The annihilator-ideal graph of $R$ is defined as the graph<br />${A_I}(R)$ with the vertex set $\Bbb A(R)^*=\Bbb A(R)\setminus\{0\}$ and two<br />distinct vertices $I$ and $J$ are adjacent if and only if<br />${\rm Ann}_R(IJ)\neq{\rm Ann}_R(I) \cup{\rm Ann}_R(J)$. In this paper, perfectness of<br />${A_I}(R)$ for some classes of rings is investigated.University of GuilanJournal of Algebra and Related Topics2345-39319120210601$n$-fold obstinate and $n$-fold fantastic (pre)filters of $EQ$-algebras3150480710.22124/jart.2021.16939.1210ENA.PaadDepartment of Mathematics, University of Bojnord, Bojnord, IranA.JafariDepartment of Mathematics, University of Bojnord, Bojnord, IranJournal Article20200628In this paper, the notions of $n$-fold obstinate and $n$-fold fantastic (pre)filter<br />in $EQ$-algebras are introduced and the relationship among $n$-fold obstinate, maximal, $n$-fold fantastic, and $n$-fold (positive) implicative prefilters are investigated. Moreover, the quotient $EQ$-algebra induced by an $n$-fold obstinate filter is studied and it is proved that the quotient $EQ$-algebra induced by<br />an $n$-fold fantastic filter of a good $EQ$-algebra with bottom element $0$ is an involutive $EQ$-algebra. Finally, the relationships between types of $n$-fold filters in residuated $EQ$-algebras is shown by diagramsUniversity of GuilanJournal of Algebra and Related Topics2345-39319120210601On beta-topological rings5160480810.22124/jart.2021.14595.1167ENS.BillawriaDepartment of Mathematics, University of Jammu, Jammu, India.Sh.SharmaDeptarment of Mathematics ,
University of Jammu, Jammu, IndiaJournal Article20191001In this paper, we introduce a generalized form of the class of topological<br /> rings, namely -topological rings by using -open sets which itself is a generalized form<br /> of open sets. Translation of open(closed) sets and multiplication by invertible elements<br /> of open(closed) sets of the -topological rings are investigated. Some other useful results<br /> on -topological rings are also given. Examples of -topological rings which fails to be<br /> topological rings are also provided. We further dene -topological rings with unity in the<br /> sequel and presented some results on it.University of GuilanJournal of Algebra and Related Topics2345-39319120210601On moduli spaces of K\"ahler-Poisson algebras over rational functions in two variables6178480910.22124/jart.2021.15242.1183ENA.Al-ShujaryDepartment of
Mathematics, Link"oping University, Link"oping, Sweden.Journal Article20191220K\"ahler-Poisson algebras were introduced as algebraic analogues of<br /> function algebras on K\"ahler manifolds, and it turns out that one<br /> can develop geometry for these algebras in a purely algebraic way. A<br /> K\"ahler-Poisson algebra consists of a Poisson algebra together with<br /> the choice of a metric structure, and a natural question arises: For<br /> a given Poisson algebra, how many different metric structures are<br /> there, such that the resulting K\"ahler-Poisson algebras are<br /> non-isomorphic? In this paper we initiate a study of such moduli<br /> spaces of K\"ahler-Poisson algebras defined over rational functions<br /> in two variables.University of GuilanJournal of Algebra and Related Topics2345-39319120210601Some results on the quotient of co-m modules7992481010.22124/jart.2021.18893.1254ENS.RajaeeDepartment of Mathematics, University
of Payame Noor,Tehran, Iran.0000-0001-8244-0752Journal Article20210211Let $R$ be a commutative ring with identity and let $M$ be a<br /> unitary $R$-module. In this paper, among various results, we prove that if $M$ is a cancellation $R$-module and $L$ is a nonzero simple submodule of $M$, then $L$ is a copure submodule of $M$. Moreover, in this case, if $M$ is co-m, then $M/L$ is also a co-m $R$-module. We investigate various conditions under which the quotient module $M/N$ of a co-m $M$ is also a co-m. We prove that if $M$ is a cancellation Noetherian co-m module, then for every second submodule $N$ of $M$ the quotient module $M/N$ is a co-m $R$-module.<br /> We obtain some results concerning socle and radical of co-m modules.University of GuilanJournal of Algebra and Related Topics2345-39319120210601The annihilator graph of modules over commutative rings93108481110.22124/jart.2021.18226.1241ENF.Esmaeili Khalil SaraeiFouman Faculty of Engineering, College of Engineering, University of Tehran, Fouman, Iran.Journal Article20201121Let $M$ be a module over a commutative ring $R$, $Z_{*}(M)$ be its set of weak zero-divisor elements, and<br />if $m\in M$, then let $I_m=(Rm:_R M)=\{r\in R : rM\subseteq Rm\}$. The annihilator graph of $M$ is the (undirected) graph<br />$AG(M)$ with vertices $\tilde{Z_{*}}(M)=Z_{*}(M)\setminus \{0\}$, and two distinct vertices $m$ and $n$ are adjacent if and<br />only if $(0:_R I_{m}I_{n}M)\neq (0:_R m)\cup (0:_R n)$. We show that $AG(M)$ is connected with diameter at most two and girth at most<br />four. Also, we study some properties of the zero-divisor graph of reduced multiplication-like $R$-modules.University of GuilanJournal of Algebra and Related Topics2345-39319120210601On CP-frames109119481210.22124/jart.2021.18801.1252ENA. A.EstajiFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, IranM.Robat SarpoushiFaculty of Mathematics and Computer Sciences,
Hakim Sabzevari University,
Sabzevar,
IranJournal Article20210202Let $\mathcal{R}_c( L)$ be the pointfree version of $C_c(X)$, the subring of $C(X)$ whose elements have countable image.<br /> We shall call a frame $L $ a $CP$-frame if the<br />ring $\mathcal{R}_c( L)$ is regular.<br /> % The main aim of this paper is to introduce $CP$-frames, that is $\mathcal{R}_c( L)$ is a regular ring. We give some<br /> We give some characterizations of $CP$-frames and we show that $L$ is a $CP$-frame if and only if each prime ideal of $\mathcal{R}_c ( L)$ is an intersection of maximal ideals if and only if every ideal of $\mathcal{R}_c ( L)$ is a $z_c$-ideal. In particular, we prove that any $P$-frame is a $CP$-frame but not conversely, in general. In addition, we study some results about $CP$-frames like the relation between a $CP$-frame $L$ and ideals of closed quotients of $L$. Next, we characterize $CP$-frames as precisely those $L$ for which every prime ideal in the ring $\mathcal{R}_c ( L)$ is a $z_c$-ideal. Finally, we show that this characterization still holds if prime ideals are replaced by essential ideals, radical ideals, convex ideals, or absolutely convex ideals.University of GuilanJournal of Algebra and Related Topics2345-39319120210601Nearrings of functions without identity determined by a single subgroup121129481310.22124/jart.2021.15730.1190ENG. AlanCannonDepartment of Mathematics,
Southeastern Louisiana University,
SLU 10687
Hammond, LA 70402,
USAV.EnlowDepartment of Mathematics,
Southeastern Louisiana University
Hammond, LA 70402,
USAJournal Article20200215Let $(G, +)$ be a finite group, written additively with identity 0, but not necessarily abelian, and let $H$ be a nonzero, proper subgroup of $G$. Then the set $M = \{f : G \to G\ |\ f(G) \subseteq H \ \hbox{and}\ f(0) = 0 \}$ is a right, zero-symmetric nearring under pointwise addition and function composition. We find necessary and sufficient conditions for $M$ to be a ring and determine all ideals of $M$, the center of $M$, and the distributive elements of $M$.University of GuilanJournal of Algebra and Related Topics2345-39319120210601On Prime and semiprime ideals of $\Gamma$-semihyperrings131141481510.22124/jart.2021.17550.1226ENJ. J.PatilIndraraj ACS college, Sillod, Dr. B. A. M. University, Aurangabad, IndiaK.PawarDepartment of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University,
Jalgaon, India0000-0002-0828-5851Journal Article20200903The $\Gamma$-semihyperring is a generalization of the concepts of a semiring, a semihyperring and a $\Gamma$-semiring. In this paper, the notions of completely prime ideals and prime radicals for $\Gamma$-semihyperring are introduced and studied some important properties accordingly. We also introduced the notions of $m$-system and complete $m$-system. Then characterizations of prime ideals and completely prime ideals of $\Gamma$-semihyperring with the help of $m$-system and complete $m$-system has been taken into account. It is our attempt to find a bridge between semiprime (completely semiprime) ideals and prime (completely prime) ideals of a $\Gamma$-semihyperring.University of GuilanJournal of Algebra and Related Topics2345-39319120210601On secondary subhypermodules143158482010.22124/jart.2021.18981.1256ENF.FarzalipourDepartment of Mathematics, Payame Noor University(PNU), Tehran, Iran.P.GhiasvandDepartment of Mathematics, Payame Noor University(PNU), Tehran, Iran.Journal Article20210221Let $R$ be a Krasner hyperring and $M$ be an $R$- hypermodule. Let $\psi: S^{h}(M)\rightarrow S^{h}(M)\cup \{\emptyset\}$ be a function, where $S^{h}(M)$ denote the set of all subhypermodules of $M$. In the first part of this paper, we introduce the concept of a secondary hypermodule over a Krasner hyperring. A non-zero hypermodule $M$ over a Krasner hyperring $R$ is called secondary if for every $r\in R$, $rM=M$ or $r^{n}M=0$ for some positive integer $n$. Then we investigate some basic properties of secondary hypermodules. Second, we introduce the notion of $\psi$-secondary subhypermodules of an $R$-hypermodule and we obtain some properties of such subhypermodules.University of GuilanJournal of Algebra and Related Topics2345-39319120210601Filtration, asymptotic $\sigma$-prime divisors and superficial elements159167482110.22124/jart.2021.17418.1221ENK. A.EssanUFR Sciences Sociales, Universite
Peleforo GON COULIBALY, Korhogo, Cote d'IvoireJournal Article20200817Let $(A,\mathfrak{M})$ be a Noetherian local ring with infinite residue field $A/ \mathfrak{M}$ and $I$ be a $\mathfrak{M}$-primary ideal of $A$. Let $f = (I_{n})_{n\in \mathbb{N}}$ be a good filtration on $A$ such that $I_{1}$ containing $I$. Let $\sigma$ be a semi-prime operation in the set of ideals of $A$. Let $l\geq 1$ be an integer and $(f^{(l)})_{\sigma} = \sigma(I_{n+l}):\sigma(I_{n})$ for all large integers $n$ and<br />$\rho^{f}_{\sigma}(A)= min \big\{ n\in \mathbb{N} \ | \ \sigma(I_{l})=(f^{(l)})_{\sigma}, for \ all \ l\geq n \big\}$. Here we show that, if $I$ contains an $\sigma(f)$-superficial element, then $\sigma(I_{l+1}):I_{1}=\sigma(I_{l})$ for all $l \geq \rho^{f}_{\sigma}(A)$. We suppose that $P$ is a prime ideal of $A$ and there exists a semi-prime operation $\widehat{\sigma}_{P}$ in the set of ideals of $A_{P}$ such that $\widehat{\sigma}_{P}(JA_{P})=\sigma(J)A_{P}$, for all ideal $J$ of $A$. Hence $Ass_{A}\big( A / \sigma(I_{l}) \big) \subseteq Ass_{A}\big( A / \sigma(I_{l+1}) \big)$, for all $l \geq \rho^{f}_{\sigma}(A)$.