Journal of Algebra and Related Topics
https://jart.guilan.ac.ir/
Journal of Algebra and Related Topicsendaily1Mon, 01 Jul 2024 00:00:00 +0330Mon, 01 Jul 2024 00:00:00 +0330On closedness of some permutative posemigroup identities
https://jart.guilan.ac.ir/article_7844.html
As we know that all non-trivial permutation identities &nbsp;are not preserved under epimorphisms of partially ordered semigroups.&nbsp; In this paper towards this open problem, first we show that certain non-trivial identities in conjunction with the permutation identity $z_1z_2 \cdots z_n=z_{i_1}z_{i_2}\cdots z_{i_n}~ &nbsp; (n\geq2)$ with $i_n \neq n &nbsp;~~[i_1 \neq 1]$ &nbsp;are preserved under epimorphisms of partially ordered semigroups. Further, we extend a result of Ahanger and Shah which showed that the center of a partially ordered semigroup $S$ is closed in $S$ and show that the normalizer of any element of a partially ordered semigroup $S$ is closed in $S$.On cohomology for module bundles over associative algebra bundles
https://jart.guilan.ac.ir/article_7845.html
We define cohomology of module bundles over associative algebra bundles. We establish a one to one correspondence between the first cohomology classes and the extensions of module bundles. Using this correspondence we give sufficient condition in terms of cohomology for an algebra bundle to be semisimple.Generalized local cohomology and Serre cohomological dimension
https://jart.guilan.ac.ir/article_7846.html
&lrm;Let $R$ be a commutative Noetherian ring, $I,~J$ be two ideals of $R$, and &nbsp;$M,~N$ be&nbsp;two $R$-modules. Let $S$ be a Serre subcategory of the category of $R$-modules.We introduce Serre cohomological dimension of $N, M$ with respect to $(I,J)$, as${\rm cd}_S(I, J, N, M)=\sup\{i\in \Bbb N_0: H_{I,J}^{i}(N, M)\not\in S\}.$We study some properties of ${\rm cd}_S(I, J, N, M)$, and we getsome formulas and upper bounds for it.
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&nbsp;A $k$-ideal-based graph of commutative semiring
https://jart.guilan.ac.ir/article_7847.html
Let $R$ be a commutative semiring and $I$ be a $k$-ideal of $R$. In this paper, we introduce the $k$-ideal-based graph of $R$, denoted by $\Gamma_{I^{*}}(R)$. The basic properties and possible structures of the graph are studied.On the m-extension dual complex Fibonacci p-numbers
https://jart.guilan.ac.ir/article_5646.html
In this paper, we introduced $m$-extension dual complex Fibonacci $p$-numbers. We established the properties of $m$-extension dual complex Fibonacci $p$-numbers. They are connected to complex Fibonacci numbers, complex Fibonacci $p$-numbers and dual complex Fibonacci $p$-numbers.On prime ideal bundles of Lie algebra bundles
https://jart.guilan.ac.ir/article_7859.html
In this paper, prime ideal bundles and semi-prime and irreducible ideal bundles of a Lie algebra bundle are defined and their relation with prime ideal bundles is studied.Modular representation of symmetric $2$-designs
https://jart.guilan.ac.ir/article_7860.html
Complementary pairs of symmetric $2$-designs are equivalent to coherent configurations of type $(2, 2; 2)$.D. G. Higman studied these coherent configurations and adjacency algebras of coherent configurations over a field of characteristic zero. These are always semisimple.&nbsp; We investigate these algebras over fields of any characteristic prime and the structures.
&nbsp;A note on generalized derivations and left ideals of prime rings
https://jart.guilan.ac.ir/article_7861.html
Let $R$ be a prime ring and $Z(R)$ denotes the center of $R$. In this study, we expose the commutativity of $R$ as a consequence of specific differential identities involving derivations acting on left ideals of $R$. Finally, we give examples that demonstrate the necessity of hypotheses taken in the theorems.On the total restrained double Italian domination
https://jart.guilan.ac.ir/article_7862.html
A double Italian &nbsp;dominating (DID) function &nbsp;of a graph $G=(V,E)$ is a function $f: V(G)\to\{0,1,2,3\}$ havingthe property that for every vertex $v\in V$, $\sum_{u\in N_G[v]}f(u)\geq 3$, if $f(v)\in \{0,1\}$.A restrained &nbsp;double Italian dominating (RDID) function is a DID function $f$ &nbsp;such that the subgraph induced by the verticeswith label $0$ has no isolated vertex.A total restrained double Italian dominating (TRDID) function is an RDID function $f$ &nbsp;such that the set $\{v\in V: f(v)&gt; 0\}$ &nbsp;induces a subgraph with no isolated vertex.\\We initiate the study of TRDID function of any graph $G$. The TRDID and RDID functions of the middle of any graph $G$ are investigated,and then, &nbsp;the sharp bounds for these parameters are established.Finally, for &nbsp;a &nbsp;graph $H$, we provide the minimum value of TRDID and RDID functions for corona graphs,$H \circ K_1$, $H \circ K_2$ and middle of them.
&nbsp;On the CD-filtration of modules with respect to a system of ideals
https://jart.guilan.ac.ir/article_7863.html
In this paper, we introduce the concept of the cohomological dimension filtration with respect to a system of ideals.In particular, a characterization of cohomological dimension filtration of a module by&nbsp;the associated prime ideals of its factors is established. As a main result, we provide a necessary and sufficient condition&nbsp;for an ascending chain of submodules of an $\mathfrak{R}$ -module $M$ to be the $\mathrm{cd}$-filtration of $M$, with respect to a system of&nbsp;ideals.
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&nbsp;Some Cayley graphs with propagation time of at most two
https://jart.guilan.ac.ir/article_7864.html
In this paper the zero forcing number as well as propagation time of $Cay(G,\Omega),$ where $G$ is a finite group and $\Omega \subset G \setminus \lbrace 1 \rbrace$ is an inverse closed generator set of $G$ is studied. In particular, it is shown that the propagation time of $Cay(G,\Omega)$ is at most two for some special generators.
&nbsp;Comaximal Intersection Graph of Ideals of Rings
https://jart.guilan.ac.ir/article_7865.html
The comaximal intersection graph $CI(R)$ of ideals of a ring $R$ is an undirected graph whose vertex set is the collection of all non-trivial (left) ideals of $R$ and any two vertices $I$ and &nbsp;$J$ are adjacent if and only if $I+J=R$ and $I\cap J\neq0$. We study the connectedness of $CI(R)$. We also discuss &nbsp;independence number, clique number, domination number, chromatic number of $CI(R)$.&nbsp;