@article { author = {Hooshmand, M.H.}, title = {Characterization and axiomatization of all semigroups whose square is group}, journal = {Algebraic Structures and Their Applications}, volume = {2}, number = {2}, pages = {1-8}, year = {2015}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {}, abstract = {In this paper we give a characterization for all semigroups whose square is a group. Moreover, we axiomatize such semigroups and study some relations between the class of these semigroups and Grouplikes,introduced by the author. Also, we observe that this paper characterizes and axiomatizes a class of Homogroups (semigroups containing an ideal subgroup).  Finally, several equivalent conditions for a semigroup $S$ with $S^2\leq S$ (the square-group property) will be considered.}, keywords = {Ideal subgroup,grouplike,homogroup,class united grouplike,real grouplike}, url = {https://as.yazd.ac.ir/article_741.html}, eprint = {https://as.yazd.ac.ir/article_741_50a5e5f483c3aa4d91f526deacc2e032.pdf} } @article { author = {VISWESWARAN, S. and PARMAR, A.}, title = {When does the complement of the annihilating-ideal graph of a commutative ring admit a cut vertex?}, journal = {Algebraic Structures and Their Applications}, volume = {2}, number = {2}, pages = {9-22}, year = {2015}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {}, abstract = { The rings considered in this article are  commutative  with identity which admit at least two  nonzero annihilating ideals. Let $R$ be a ring. Let $\mathbb{A}(R)$ denote the set of all annihilating ideals of $R$ and let $\mathbb{A}(R)^{*} = \mathbb{A}(R)\backslash \{(0)\}$. The annihilating-ideal graph of $R$, denoted by $\mathbb{AG}(R)$  is an undirected simple graph whose vertex set is $\mathbb{A}(R)^{*}$ and distinct vertices $I, J$ are joined by an edge in this graph if and only if $IJ = (0)$. The aim of this article is to classify rings  $R$ such that $(\mathbb{AG}(R))^{c}$ ( that is,  the complement of $\mathbb{AG}(R)$)   is connected and admits a cut vertex.}, keywords = {N-prime of $(0)$,B-prime of $(0)$,complement of the annihilating-ideal graph of a commutative ring,vertex cut and cut vertex of a connected graph}, url = {https://as.yazd.ac.ir/article_765.html}, eprint = {https://as.yazd.ac.ir/article_765_b8befa609c45c0b6b6a79bc456253b4a.pdf} } @article { author = {Saidi Goraghani, Simin and Borzooei, Rajab ali}, title = {Ultra and Involution Ideals in $BCK$-algebras}, journal = {Algebraic Structures and Their Applications}, volume = {2}, number = {2}, pages = {23-36}, year = {2015}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {}, abstract = {In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the notions of prime ideals and ultra ideals are coincide.}, keywords = {$BCK$-algebra,(associative,commutative,positive implicative,implicative) ideal,ultra ideal,involution ideal}, url = {https://as.yazd.ac.ir/article_784.html}, eprint = {https://as.yazd.ac.ir/article_784_59ea8d93f1f07746b0ae002a32a6a389.pdf} } @article { author = {Arabyani, Homayoon and Fadravi, Hadi Hosseini}, title = {The structure of a pair of nilpotent Lie algebras}, journal = {Algebraic Structures and Their Applications}, volume = {2}, number = {2}, pages = {37-47}, year = {2015}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {}, abstract = {Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $\mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpotent Lie algebras and generalize results for a pair of non-abelian nilpotent Lie algebras.}, keywords = {Nilpotent Lie algebra,Pair of Lie algebras,Schur multiplier}, url = {https://as.yazd.ac.ir/article_785.html}, eprint = {https://as.yazd.ac.ir/article_785_f8abf078bb44933f3c1b0a1d39b66275.pdf} } @article { author = {Hadjirezaei, Somayeh and Karimzadeh, Somayeh}, title = {On the nil-clean matrix over a UFD}, journal = {Algebraic Structures and Their Applications}, volume = {2}, number = {2}, pages = {49-55}, year = {2015}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {}, abstract = { In this paper we characterize all $2\times 2$ idempotent and nilpotent matrices over an integral domain and then we characterize all $2\times 2$ strongly nil-clean matrices over a PID. Also, we determine when a $2\times 2$ matrix  over a UFD is nil-clean.}, keywords = {Rank of a matrix,Idempotent matrix,Nilpotent matrix,Nil-clean matrix,Strongly nil-clean matrix}, url = {https://as.yazd.ac.ir/article_803.html}, eprint = {https://as.yazd.ac.ir/article_803_7a98829c79d5ccc6521ac399e996e7bb.pdf} } @article { author = {Mohamadian, Rostam}, title = {$z^\circ$-filters and related ideals in $C(X)$}, journal = {Algebraic Structures and Their Applications}, volume = {2}, number = {2}, pages = {57-66}, year = {2015}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {}, abstract = {In this article we introduce the concept of $z^\circ$-filter on a topological space $X$. We study and investigate the behavior of $z^\circ$-filters and compare them  with corresponding ideals, namely, $z^\circ$-ideals of $C(X)$,  the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^\circ$-filter is ci-fixed. Finally, by using  $z^\circ$-ultrafilters, we prove that any arbitrary product of i-compact spaces is i-compact.}, keywords = {$z^circ$-filter,prime $z^circ$-filter,ci-free $z^circ$-filter,i-free $z^circ$-filter,$z^circ$-ultrafilter,i-compact}, url = {https://as.yazd.ac.ir/article_807.html}, eprint = {https://as.yazd.ac.ir/article_807_bb25ddc73dfd82df981f87a48bcc5e25.pdf} }