Yazd UniversityAlgebraic Structures and Their Applications2382-976111120240201A class of almost uniserial rings19334410.22034/as.2024.3344ENHamid RezaDorbidiDepartment of Mathematics, Faculty of Science, University of Jiroft, P.O. Box 78671-61167, Jiroft, Iran.Journal Article20211112An $R-$module $M$ is called almost uniserial if any two non-isomorphic submodules of $M$ are comparable. A ring $R$ is an almost left uniserial ring if $_R R$ is almost uniserial. In this paper, we introduce a class of artinian almost uniserial rings. Also we give a classification of almost uniserial modules over principal ideal domains.https://as.yazd.ac.ir/article_3344_8b1e358b2a6a1e3ffc2fd45f5dc3e1bd.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976111120240201Local automorphisms of $n$-dimensional naturally graded quasi-filiform Leibniz algebra of type I1124335010.22034/as.2023.18189.1517ENJobirAdashevV. I. Romanovskiy Institute of Mathematics, University Street 9, Tashkent, 100174, Uzbekistan
and Chirchiq State Pedagogical University, Amir Temur Street 104, 111700, Uzbekistan.0000-0002-4882-4098BakhtiyorYusupovV. I. Romanovskiy Institute of Mathematics, University Street 9, Tashkent, 100174, Uzbekistan
and Urgench State University, H. Alimdjan street 14, Urgench, 220100, Uzbekistan.Journal Article20220311The notions of a local automorphism for Lie algebras are defined as similar to the associative case. Every automorphism of a Lie algebra $\mathcal{L}$ is a local automorphism. For a given Lie algebra $\mathcal{L}$, the main problem concerning these notions is to prove that they automatically become an automorphism or to give examples of local automorphisms of $\mathcal{L}$, which are not automorphisms. In this paper, we study local automorphisms on quasi-filiform Leibniz algebras. It is proved that quasi-filiform Leibniz algebras of type I, as a rule, admit local automorphisms which are not automorphisms.https://as.yazd.ac.ir/article_3350_f8f317457dff8c084f422be862dc9dac.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976111120240201On the genus of annihilator intersection graph of commutative rings2536335110.22034/as.2023.18830.1573ENMohdNazimDepartment of Mathematics, Aligarh Muslim University, Aligarh-202002, India.Nadeem UrRehmanDepartment of Mathematics, Aligarh Muslim University, Aligarh-202002, India.0000-0003-3955-7941K.SelvakumarDepartment of Mathematics, Manonmaniam Sundaranar University, Tirunelveli-627012, India.Journal Article20220809Let $R$ be a commutative ring with unity and $A(R)$ be the set of annihilating-ideals of $R$. The annihilator intersection graph of $R$, represented by $AIG(R)$, is an undirected graph with $A(R)^*$ as the vertex set and $\mathfrak{M} \sim \mathfrak{N}$ is an edge of $AIG(R)$ if and only if $Ann(\mathfrak{M}\mathfrak{N}) \neq Ann(\mathfrak{M}) \cap Ann(\mathfrak{N})$, for distinct vertices $\mathfrak{M}$ and $\mathfrak{N}$ of $AIG(R)$. In this paper, we first defined finite commutative rings whose annihilator intersection graph is isomorphic to various well-known graphs, and then all finite commutative rings with a planar or toroidal annihilator intersection graph were characterized.https://as.yazd.ac.ir/article_3351_57a1078843263fb9069b4f16ccc5528d.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976111120240201Hybrid ideals on a lattice3753335210.22034/as.2023.19575.1612ENS.MeenakshiDepartment of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore 641 114, Tamilnadu, India.0000-0003-0720-3647Young BaeJunDepartment of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea.0000-0002-0181-8969Seok-ZunSongDepartment of Mathematics, Jeju National University, Jeju 63243, Korea.0000-0002-2383-664XBElavarasanDepartment of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore 641 114, Tamilnadu, India.0000-0002-1414-2814Journal Article20230118The fuzzy set is a fantastic tool for expressing hesitancy and dealing with uncertainty in real-world circumstances. Soft set theory has recently been developed to deal with practical problems. The soft and fuzzy sets were combined by Jun et al. to generate hybrid structures. The idea of hybrid ideals on a distributive lattice is discussed in this work. The relation between hybrid congruences and hybrid ideals on a distributive lattice is also examined. In addition, the product of hybrid ideals and its numerous results are discussed.https://as.yazd.ac.ir/article_3352_bbbe733d5b57a0f7435e8c7a6981fd16.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976111120240201On higher order $z$-ideals and $z^\circ$-ideals in commutative rings5561319610.22034/as.2023.18637.1553ENRostamMohamadianDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran.0000-0003-3350-366XJournal Article20220622A ring $R$ is called radically $z$-covered (resp. radically $z^\circ$-covered) if every $\sqrt z$-ideal (resp. $\sqrt {z^\circ}$-ideal) in $R$ is a higher order $z$-ideal (resp. $z^\circ$-ideal). In this article we show with a counter-example that a ring may not be radically $z$-covered (resp. radically $z^\circ$-covered). Also a ring $R$ is called $z^\circ$-terminating if there is a positive integer $n$ such that for every $m\geq n$, each $z^{\circ m}$-ideal is a $z^{\circ n}$-ideal. We show with a counter-example that a ring may not be $z^\circ$-terminating. It is well known that whenever a ring homomorphism $\phi:R\to S$ is strong (meaning that it is surjective and for every minimal prime ideal $P$ of $R$, there is a minimal prime ideal $Q$ of $S$ such that $\phi^{-1}[Q] = P$), and if $R$ is a $z^\circ$-terminating ring or radically $z^\circ$-covered ring then so is $S$. We prove that a surjective ring homomorphism $\phi:R\to S$ is strong if and only if ${\rm ker}(\phi)\subseteq{\rm rad}(R)$.https://as.yazd.ac.ir/article_3196_3dd8087f904f2fb57643cb21efc3eada.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976111120240201Some results on the strongly annihilating submodule graph of a module6378311710.22034/as.2023.17624.1481ENRezaBeyranvandDepartment of Mathematics, Lorestan university, Khoramabad, Iran.ParvinKarimi BeiranvandDepartment of Mathematics, Islamic Azad University, Khorramabad branch, Khoramabad, Iran.Journal Article20211117Let M be a module over a commutative ring R. We continue our study of strongly annihilating submodule graph SAG(M) introduced in [9]. In addition to providing the more properties of this graph, we introduce the subgraph SAG∗(M) of SAG(M) and compare the properties of SAG∗(M) with SAG(M) and AG(M) (the annihilating submodule graph<br />of M introduced in [5])https://as.yazd.ac.ir/article_3117_fa4a4fb3a7f93c53f8c8a34bfae882cb.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976111120240201Right-left induced hyperlattices and the genetic code hyperlattices7998312310.22034/as.2023.18716.1562ENMortezaJafarpourDepartment of Mathematics, Vali-e-Asr university of Rafsanjan, Rafsanjan, Iran.AliZolfaghariDepartment of Mathematics, Vali-e-Asr university of Rafsanjan, Rafsanjan, Iran.Journal Article20220710In this paper first we introduce right(resp. left) induced hyperlattices and investigate some of their properties. Especially a characterization of the smallest strongly regular relation for the class of distributive right/left induced hyperlattice is investigated. Next we propose and study the generated hyperlattices from hyperlattices. Finally, the right induced hyperlattices of two Boolean lattices of four DNA bases and physico-chemical properties of amino acids of four DNA bases are investigated.https://as.yazd.ac.ir/article_3123_96a6ad6df340aa48014473fdac8168a8.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976111120240201The duals of annihilator conditions for modules99113313910.22034/as.2023.18995.1588ENFaranakFarshadifarDepartment of Mathematics Education, Farhangian University, P. O. Box 14665-889, Tehran, Iran.Journal Article20220917Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. The purpose of this paper is to introduce and investigate the submodules of an $R$-module $M$ which satisfy the dual of Property $\mathcal{A}$, the dual of strong Property $\mathcal{A}$, and the dual of proper strong Property $\mathcal{A}$. Moreover, a submodule $N$ of $M$ which satisfy Property $\mathcal{S_J(N)}$ and Property $\mathcal{I^M_J(N)}$ will be introduced and investigated.https://as.yazd.ac.ir/article_3139_4cebfeeb005c1f7e0b299308c40452c8.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976111120240201Modular group algebra with upper Lie Nilpotency index $11p-9$115130314010.22034/as.2023.17039.1440ENKuldeepSinghDepartment of Mathematics and Scientific Computing, M. M. M. University of Technology, Gorakhpur, India.HarishChandraDepartment of Mathematics and Scientific Computing, M. M. M. University of Technology, Gorakhpur, India.0000-0001-5232-6043SuchiBhattDepartment of Mathematics and Scientific Computing, MMM University of Technology, GorakhpurJournal Article20210725Let $KG$ be the modular group algebra of a group $G$ over a field $K$ of characteristic $p>0$. Recently, we have seen the classification of group algebras $KG$ with upper Lie nilpotency index $t^{L}(KG)$ up to $10p-8$. In this paper, our aim is to classify the modular group algebra $KG$ with upper Lie nilpotency index $11p-9$, for $G'= \gamma_{2}(G)$ as an abelian group.https://as.yazd.ac.ir/article_3140_6f035e24a90ebf46be56d0f57243d79c.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976111120240201A study on constacyclic codes over the ring $\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$131150314510.22034/as.2023.3145ENSt TimothyKomDepartment of Mathematics, Manipur University, Imphal, Manipur-795003, India.O. RatnabalaDeviDepartment of Mathematics, Manipur University, Imphal, Manipur-795003, India.Th. RojitaChanuDepartment of Mathematics, D. M. College of Science, Imphal, Manipur-795001, India.Journal Article20210417This paper studies $\lambda$-constacyclic codes and skew $\lambda$-constacyclic codes over the finite commutative non-chain ring $R=\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$ with $u^3=0$ for $\lambda= (1+2u+2u^2)$ and $(3+2u+2u^2)$. We introduce distinct Gray maps and show that the Gray images of $\lambda$-constacyclic codes are cyclic, quasi-cyclic, and permutation equivalent to quasi-cyclic codes over $\mathbb{Z}_4$. It is also shown that the Gray images of skew $\lambda$-constacyclic codes are quasi-cyclic codes of length $2n$ and index 2 over $\mathbb{Z}_4$. Moreover, the structure of $\lambda$-constacyclic codes of odd length $n$ over the ring $R$ is determined and give some suitable examples.https://as.yazd.ac.ir/article_3145_cd7c215299c71d8ec7f8c292ffd2993d.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976111120240201Semihypergroups that every hyperproduct only contains some of the factors151163315010.22034/as.2023.17037.1439ENDariushHeidariFaculty of science,
Mahallat Institute of Higher Education, Mahallat, IranJournal Article20210724Breakable semihypergroups, defined by a simple property: every non-empty subset of them is a subsemihypergroup. In this paper, we introduce a class of semihypergroups, in which every hyperproduct of $n$ elements is equal to a subset of the factors, called $\pi_n$-semihypergroups. Then, we prove that every semihypergroup of type $\pi_{2k}$, ($k\geq 2$) is breakable and every semihypergroup of type $\pi_{2k+1}$ is of type $\pi_3$. Furthermore, we obtain a decomposition of a semihypergroup of type $\pi_n$ into the cyclic group of order 2 and a breakable semihypergroup. Finally, we give a characterization of semi-symmetric semihypergroups of type $\pi_n$.https://as.yazd.ac.ir/article_3150_9f30e8baf0bca7f2d5982f1610e420b6.pdfYazd UniversityAlgebraic Structures and Their Applications2382-976111120240201On the Ree groups $^2{}G_2(q)$ characterized by a size of a conjugacy class165171315110.22034/as.2023.19014.1589ENBehnamEbrahimzadehState Office of Education in Qaemiyeh, Fars Province, Iran.0000-0001-5696-275xAhmadKhaksariDepartment of Mathematics, Payame Noor University, P. Box: 19395-3697, Tehran, Iran.Journal Article20220921One of the important problem in finite groups theory is group characterization by specific property. Properties, such as element order, the set of element with the same order, etc. In this paper, we prove that Ree group $^2{}G_2(q)$, where $q\pm\sqrt{3q}+1$ is a prime number can be uniquely determined by its order and one conjugacy class size.https://as.yazd.ac.ir/article_3151_5f251d8243a8bf50cdda418e8c3c70c3.pdf