Algebraic Structures and Their Applications
http://as.yazd.ac.ir/
Algebraic Structures and Their Applicationsendaily1Tue, 09 Aug 2022 00:00:00 +0430Tue, 09 Aug 2022 00:00:00 +0430$\Lambda$-Extension of binary matroids
http://as.yazd.ac.ir/article_2608.html
In this paper, we combine two binary operations $\Gamma$-Extension and element splitting under special conditions, to extend binary matroids. For a given binary matroid $M$, we call a matroid obtained in this way a $\Lambda$-Extension of $M$. We note some attractive properties of this matroid operation, particularly constructing a chordal matroid from a chordal binary matroid.GE-derivations
http://as.yazd.ac.ir/article_2631.html
The notions of $\xi$-inside GE-derivation and $\xi$-outside GE-derivation on a GE-algebra are introduced and its properties are investigated. Conditions for a self-map on GE-algebra to be a $\xi$-inside GE-derivation and a $\xi$-outside GE-derivation are provided. The $\xi$-inside GE-derivation or the $\xi$-outside GE-derivation $\varrho$ are used to form two sets $X_{(\varrho = \xi)}$ and ${\rm ker}(\varrho)$, and GE-subalgebra and GE-filter are studied for these two sets.Some separation axioms in topoframes
http://as.yazd.ac.ir/article_2653.html
This paper is about the extension of some classical separation axioms Hausdorffness, regularity and complete regularity to topoframes. We show that they agree with those in frames except perhaps for complete regularity. The interesting results are about complete regularity, in particular when and how these differ from the frame results. These together with the results about B-filters are the focus of the paper.Characterization of monoids by a generalization of weak flatness property
http://as.yazd.ac.ir/article_2655.html
In [On a generalization of weak flatness property, Asian-European Journal of Mathematics, 14(1) (2021)] we introduce a generalization of weak flatness property, called $(WF)'$, and showed that a monoid $S$ is absolutely $(WF)'$ if and only if $S$ is regular and satisfies Conditions $(R_{(WF)'})$ and $(L_{(WF)'})$. In this paper we continue the characterization of monoids by this property of their (finitely generated, (mono)cyclic, Rees factor) right acts. Also we give a classification of monoids for which $(WF)'$ property of their (finitely generated, (mono)cyclic, Rees factor) right acts imply other properties and vise versa. The aim of this paper is to show that the class of absolutely $(WF)'$ monoids and absolutely (weakly) flat monids are coincide.Binary block-codes of $MV$-algebras and Fibonacci sequences
http://as.yazd.ac.ir/article_2671.html
In this paper, the notion of an $M$-function and cut function on a set are introduced and investigated several properties. We use algebraic properties to introduce an algorithm which show that every finite $MV$-algebras and Fibonacci sequences determines a block-code and presented some connections between Fibonacci sequences, $MV$-algebras and binary block-codes. Furthermore, an $MV$-algebra arising from block-codes is established.On the essential $CP$-spaces
http://as.yazd.ac.ir/article_2674.html
Let $C_c(X)$ be the functionally countable subalgebra of $C(X)$. Essential $CP$-spaces are introduced and investigated algebraically and topologically. It is shown that if $X$ is a proper essential $CP$-space, then $mC_c(X)$ is compact if and only if $\{ \eta \}$ is a $G_\delta$, where $\eta$ is the only non $CP$-point of $X$ and $mC_c(X)$ is the space of minimal prime ideals of $C_c(X)$ which are not maximal. Quasi $F_c$-spaces, $c$-basically disconnect spaces, almost $CP$-spaces and almost essential $CP$-spaces are introduced and studied via essential $CP$-spaces. Finally, $C_c(X)$ as a $CSV$-ring where $X$ is an essential $CP$-space is investigated.A new characterization of Projective Special Unitary groups $\mathbf{ U_3 (3^n )}$ by the order of group and the number of elements with the same order
http://as.yazd.ac.ir/article_2675.html
In this paper, we prove that projective special unitary groups $U_3 (3^n)$, where $ 3^{2n}-3^{n}+1$ is a prime number and $3^n\equiv\pm2(\mod 5)$, can be uniquely determined by the order of group and the number of elements with the same order.Modules whose surjective endomorphisms have a $\gamma$-small kernels
http://as.yazd.ac.ir/article_2677.html
In this paper, we introduce a proper generalization of that of Hopfian modules, called $\gamma$-Hopfian modules. A right $R$-module $M$ is said to be $\gamma$-Hopfian, if any surjective endomorphism of $M$ has a $\gamma$-small kernel. Some basic characterizations of $\gamma$-Hopfian modules are proved. We prove that a ring $R$ is semisimple cosingular if and only if every $R$-module is $\gamma$-Hopfian. Further, we prove that the $\gamma$-Hopfian property is preserved under Morita equivalences. Some other properties of $\gamma$-Hopfian modules are also obtained with examples.r-notion of Conjugacy in Partial and Full Injective Transformations
http://as.yazd.ac.ir/article_2693.html
In this paper, we define a new notion of conjugacy in semigroups that reduces to the n-notion of conjugacy in an inverse semigroup. We compare our new notion with the existing notions. We characterize the notion in partial injective and in full injective transformations and determine the conjugacy classes in these semigroups.Characterizations of $J$-prime ideals and $M_{J}$-ideals in posets
http://as.yazd.ac.ir/article_2719.html
In this paper, we introduce the concepts of $J$-prime ideals and $M_{J}$-ideals in posets, and obtain some of their interesting characterizations in posets. Furthermore, we discuss the properties of $J$-ideals that are analogous to $J$-prime ideals and $M_J$-ideals in posets. Finally, we establish a set of equivalent conditions for an ideal in a poset $\mathcal{P}$ containing an ideal $J$ is an $J$-ideal, and for a semi-prime ideal $J$ to be an $M_{J}$-ideal of $\mathcal{P}$.A note on $\sigma$-ideals of distributive lattices
http://as.yazd.ac.ir/article_2720.html
Some properties of $\sigma$-ideals of distributive lattices are studied. The classes of Boolean algebras, generalized Stone lattices, relatively complemented lattices are characterized with the help of $\sigma$-ideals and maximal ideals. Some significant properties of prime $\sigma$-ideals are studied with the help of a congruence.Some Remarks on $(\operatorname{INC}(R))^{c}$
http://as.yazd.ac.ir/article_2728.html
Let $R$ be a commutative ring with identity $1 \neq 0$ which admits at least two maximal ideals. In this article, we have studied simple, undirected graph $(\operatorname{INC}(R))^{c}$ whose vertex set is the set of all proper ideals which are not contained in $J(R)$ and two distinct vertices $I_{1}$ and $I_{2}$ are joined by an edge in $(\operatorname{INC}(R))^{c}$ if and only if $I_{1} \subseteq I_{2}$ or $I_{2} \subseteq I_{1}$. In this article, we have studied some interesting properties of $(\operatorname{INC}(R))^{c}$.The Noetherian dimension of modules versus their $\alpha$-small shortness
http://as.yazd.ac.ir/article_2699.html
In this article, we first consider concept of small Noetherian dimension of a module, which is dual to the small krull dimension, denoted by $sn{\rm -dim}\, A$, and defined to be the codeviation of the poset of the small submodules of $A$. We prove that if an $R$-module $A$ with finite hollow dimension, has small Noetherian dimension, then $A$ has Noetherian dimension and $ sn{\rm -dim}\, A\leq n{\rm -dim}\, A\leq sn{\rm -dim}\, A+1$. Last we introduce the concept of $\alpha$-small short modules, i.e., for each small submodule $S$ of $A$, either $n{\rm -dim}\, S \leqslant \alpha$ or $sn{\rm -dim}\,\frac{A}{S}\leqslant\alpha$ and $\alpha$ is the least ordinal number with this property and by using this concept, we extend some of the basic results of short modules to $\alpha$-small short modules. In particular, we prove that if $A$ is an $\alpha$-small short module, then it has small Noetherian dimension and $sn{\rm -dim}\, A=\alpha$ or $sn{\rm -dim}\, A=\alpha+1$. Consequently, we show that if $A$ is an $\alpha$-small short module with finite hollow dimension, then $\alpha\leq n{\rm -dim}\, A\leq\alpha+2$.On GE-ideals of bordered GE-algebras
http://as.yazd.ac.ir/article_2700.html
In this paper, the properties of GE-ideals of transitive bordered GE-algebra are studied and characterizations of GE-ideals are given. We have observed that the set of all GE-ideals of a transitive bordered GE-algebra forms a complete lattice. The notion of bordered GE-morphism is introduced and established fundamental bordered GE-morphism theorem. A congruence relation on a bordered GE-algebra with respect to GE-ideal is introduced and some bordered GE-morphism theorems are derived.Laplacian spectral characterization of setosa graphs
http://as.yazd.ac.ir/article_2703.html
A setosa graph $SG(e,f,g,h,d;b_1,b_2,\ldots,b_s)$ is a graph consisting of five cycles and $s(\geq 1)$ paths $P_{b_1+1}, P_{b_2+1},\ldots,P_{b_s+1}$ intersecting in a single vertex that all meet in one vertex, where $b_i\geq1$ (for $i=1,\ldots,s$) and $e,f,g,h,d\geq 3$ denote the length of the cycles $C_e$, $C_f$, $C_g$, $C_h$ and $C_d$, respectively. Two graphs $G$ and $H$ are $L$-cospectral if they have the same Laplacian spectrum. A graph $G$ is said to be determined by the spectrum of its Laplacian matrix (DLS, for short) if every graph with the same Laplacian spectrum is isomorphic to $G$. In this paper we prove that if $H$ is a $L$-cospectral graph with a setosa graph $G$, then $H$ is also a setosa graph and the degree sequence of $G$ and $H$ are the same. We conjecture that all setosa graphs are DLS.Sums of units in Baer and exchange rings
http://as.yazd.ac.ir/article_2721.html
In this paper, we prove that every element in an exchange ring $R$ with artinian primitive factors is $n$-tuplet-good iff $1_R$ is $n$-tuplet-good. Also, we show that for such rings the full matrix ring $M_n(R)$ (for $n\geq 2$) is $n$-tuplet-good. In [7], Fisher and Snider proved that every element of a strongly $\pi$-regular ring $R$ with $\frac{1}{2}\in R$ is 2-good. We prove the same result under new condition and show that these rings are twin-good. We also consider the conditions under which endomorphism ring of a finitely generated projective module $M$ over unit regular ring $L$ is 2-tuplet-good. The main result of [14] states that regular self-injective rings are $n$-tuplet-good if such rings has no factor ring isomorphic to a field $D$ with $|D|&lt;n+2$. We generalized this result to regular Baer rings proving that every regular Baer ring $R$ that has no factor ring isomorphic to a field of order less than $n+2$, is $n$-tuplet-good.On $\sim_{n}$ notion of conjugacy in Semigroups
http://as.yazd.ac.ir/article_2724.html
In this paper, we study the $\sim_{n}$ notion of conjugacy in semigroups. After proving some basic results, we characterize this notion in subsemigroups of $\mathcal{P}(T)$ (partial transformation semigroup) and $\mathcal{T}(T)$ (transformation semigroup) through digraphs and their restrictive partial homomorphisms.On the power graphs of finite groups and Hamilton cycle
http://as.yazd.ac.ir/article_2748.html
The power graph $\mathcal{P}(G)$ of a finite group $G$ is a graph whose vertex set is the group $G$ and distinct elements $x,y\in G$ are adjacent if one is a power of the other, that is, $x$ and $y$ are adjacent if $x\in \langle y\rangle$ or $y \in \langle x\rangle$. In this paper, we study existence of the Hamilton cycle in the power graph of some finite nilpotent groups $G$ with a cyclic subgroup as direct factor when $G$ is written as direct product Sylow $p$-subgroups. For this purpose we use of cartesian product a spanning tree and a cycle. Finally, we determined values of $n$ such that $\mathcal{P}(U_n)$ is Hamiltonian, where $U_n$ is a group consist of all positive integers less than $n$ and relatively prime to $n$ under multiplication modulo $n$.&nbsp;Some results of $\alpha$-coset groups
http://as.yazd.ac.ir/article_2806.html
We call $G$ to be an $\alpha$-coset group, if it contains a proper $\alpha$-invariant normal subgroup $N$ such that $Nx^\alpha =\{x^g~|~ g\in G\}$, for some automorphism $\alpha$ of $G$ and any $x \in G\setminus N$. Clearly, if $\alpha$ is identity automorphism of $G$, one obtains the notion of con-cos groups, which was first introduced by Muktibodh in 2006.In the present article, we discuss some properties of the new notion. Also, we introduce the concept of $\alpha$-Camina groups and give its connection with the groups of property $\mathcal P$, where $\mathcal P$ is the class of all finite groups such that their $\alpha$-centres are the same as $\alpha$-commutator subgroups of order $p$.Some results on uniform MV-algebras
http://as.yazd.ac.ir/article_2818.html
In this paper, we study Tychonoff spaces and uniformities on MV-algebras. In particular, we find some conditions under which an MV-algebra can be made into a Tychonoff space. Also, we find uniformities that make an MV-algebra into a uniform MV-algebra. Next, we discuss some algebraic and topological properties of uniform MV-algebras. More precisely, we study the existence of closed ideals and closed filters, and examine the way these are related to uniform MV-algebras. Furthermore, we obtain some results on the uniform continuity of the operations and its consequences.&nbsp;Minimal Prime Filters of Commutative $BE$-Algebras
http://as.yazd.ac.ir/article_2840.html
In this paper we introduced the concept of minimal prime filters in commutative $BE$-algebras. A characterization theorem for minimal prime filters of $BE$-algebras is derived. Some properties of minimal prime filters of a commutative $BE$-algebras are derived with the help of congruences. A necessary and sufficient is derived for a pair of minimal prime filters to become co-maximal.On the basic properties of the Compressed annihilator graph of $\mathbb{Z}_n$
http://as.yazd.ac.ir/article_2843.html
For a commutative ring $R$, the compressed annihilator graph $AG_E(R)$ is defined by, taking the equivalence classes of zero divisors of $R$ as the vertex set and two distinct vertices $[a]$ and $[b]$ are adjacent if and only if $ ann(a) \cup ann (b) \subset ann(ab)$. In this paper, we discuss some of the basic properties such as degree of the vertices, Eulerian, regularity, domination number and planarity of $AG_E(\mathbb{Z}_n)$, where $\mathbb{Z}_n$ is the ring of integer modulo $n$.