University of GuilanJournal of Algebra and Related Topics2345-39319220211201Semi-topological UP-algebras122515210.22124/jart.2021.18760.1249ENA. B.KhalafDepartment of
Mathematics, College of Science, University
of Duhok, Kurdistan Region, Iraq.0000-0002-9626-6908M. A.YousefDepartment of
Mathematics, College of Basic Education, University
of Duhok, Kurdistan Region, IraqJournal Article20210129The aim of this paper is to study the concept of semi-topological UP-algebras which is a UP-algebra supplied with a certain type of topology that makes the binary operation defined on it semi-topologically continuous. This concept is a generalization of the concept of topological UP-algebra. We obtain several properties of semi-topological UP-algebras . Furthermore, we introduce and study the concepts of semi(resp., s, irresolute)-topological UP-homomorphisms and some topological structures on certain types of UP-algebras.https://jart.guilan.ac.ir/article_5152_4539ac967420a1ee6385956f0c1304f3.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39319220211201On Characteristic Ideal Bundles of a Lie Algebra Bundle2328518210.22124/jart.2021.17340.1218ENR.KumarDepartment of Mathematics, School of Applied Sciences
REVA University, Bengaluru-560064, IndiaJournal Article20200810We show that, every derivation of a Lie algebra bundle can be viewed as an inner derivation if one embeds the Lie algebra bundle into a larger Lie algebra bundle. We define, the radical and the nilradical bundle of a Lie algebra bundle and prove, both are characteristic ideal bundles of Lie algebra bundle.https://jart.guilan.ac.ir/article_5182_c508584a5187c9e3f459a0e0c942d9b7.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39319220211201BZS Rings, II2937518310.22124/jart.2021.17183.1212ENM.FaragDepartment of Mathematics, Fairleigh Dickinson University, 1000 River Rd, Tea-neck, NJ, 07666, USA.R. P.TucciDepartment of Mathematics and Computer Science, Loyola University New Orleans, New Orleans, LA, USA.Journal Article20200723An associative ring R, not necessarily commutative and not necessarily with identity, is called Boolean-zero square or<br />BZS if every element of R is either idempotent or nilpotent of index 2. We continue our investigation of the structure of nite<br />BZS rings.https://jart.guilan.ac.ir/article_5183_2af09a2ccc1a630087acf30993556041.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39319220211201Conjectures of Ene, Herzog, Hibi, and Saeedi Madani in the {\sl Journal of Algebra}3946518410.22124/jart.2021.20356.1305ENJ. D.FarleyDepartment of
Mathematics, Morgan State University, 1700 E. Cold
Spring Lane, Baltimore, USA.0000-0003-3247-6014Journal Article20210811In the preprint of ``Pseudo-Gorenstein and Level Hibi Rings,'' Ene, Herzog, Hibi, and Saeedi Madani assert (Theorem 4.3) that for a regular planar lattice $L$ with poset of join-irreducibles $P$, the following are equivalent:<br />(1) $L$ is level;<br />(2) for all $x,y\in P$ such that $y\lessdot x$, $\height_{\hat P}(x)+\depth_{\hat P}(y)\le\rank(\hat P)+1$;<br />(3) for all $x,y\in P$ such that $y\lessdot x$, either $\depth(y)=\depth(x)+1$ or $\height(x)=\height(y)+1$.<br />They added, ``Computational evidence leads us to conjecture that the equivalent conditions given in Theorem 4.3 do hold for any planar lattice (without any regularity assumption).''<br />Ene {\sl et al.} prove the equivalence of (2) and (3) for a regular simple planar lattice, and write, ``One may wonder whether the regularity condition ... is really needed.''<br />We show one cannot drop the regularity condition. <br /><br />Ene {\sl et al.} say that ``we expect'' (2) to imply (1) for any finite distributive lattice $L$.<br /><br />We provide a counter-example.https://jart.guilan.ac.ir/article_5184_c9447ccc21ee53f81415d443ad81b1a9.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39319220211201On 2-absorbing and weakly 2-absorbing principally right primary ideals4767518510.22124/jart.2021.19172.1264ENN. J.GroenewaldDepartment of Mathematics, Nelson Mandela University, Port Elizabeth, South Africa.000-0003-2843-3046Journal Article20210314Let R be a noncommutative ring. The purpose of this note is to investigate the concept of 2-absorbing (resp., weakly 2-absorbing) p right primary ideals generalizing 2-absorbing (resp., weakly 2-absorbing) ideals of noncommutative rings. From Birkenmeier we have that for commutative rings the notions of primary rings (ideals) coincide with p right primary rings (ideals). Hence all results about 2-absorbing and weakly 2-absorbing primary ideals for commutative rings will follow as special cases from results proved in this note. A number of results concerning 2-absorbing (resp., weakly 2-absorbing) p right primary ideals are given, generalizing the corresponding results from commutative rings to noncommutative rings.https://jart.guilan.ac.ir/article_5185_59cd6fb009267c42d07de1ba5a6f074d.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39319220211201On e-small Compressible Modules6981518610.22124/jart.2021.19462.1269ENP. Ch.DiopDepartment of Mathematics, UFR SET, Iba Der Thiam University , Thies, Senegal.0000-0003-0628-0018M. L.DiaDepartment of Mathematics, faculty of Science, Cheikh Anta Diop University,
Dakar, Senegal.Journal Article20210428Let $R$ be a commutative ring with identity and let M be an (left) unitary $R$-module. In this paper, we introduce a detail and study the concept of e-small compressible as a generalization of the compressible module, and give some of their properties, characterizations, and examples. On the other hand, we study the relations between e-small compressible modules and some classes of modules.https://jart.guilan.ac.ir/article_5186_3a73a2824feeba56d314b1a2d7e09045.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39319220211201On Closed Homotypical Varieties of Semigroups8395518710.22124/jart.2021.18949.1255ENSh.AbbasDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaW.AshrafDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaN. NoorRafiqueeDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaJournal Article20210216It is known that all subvarieties of the variety of all semigroups are not absolutely closed. So, we determine some closed homotypical varieties of semigroups determined by the identities $axy=x^2ayx$, $axy=xa^2ya$, $axy=yay^2x$, $axy=xaya^2$, $axy=y^2ayx$ and $axy=xayx^2$.https://jart.guilan.ac.ir/article_5187_d3e0ea1a8a98a336c730ae64260a828e.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39319220211201Valuation near rings95100530110.22124/jart.2021.19101.1261ENE.KhodadadpourDepartment of
Mathematics, Kerman Branch, Islamic Azad University
Kerman, IranT.RoodbarylorDepartment of Mathematics, Kerman Branch, Islamic Azad University Kerman, IranJournal Article20210307In this paper, the authors have defined the valuation near ring. They have proved some<br />theorem, for example, they have shown every valuation near ring is a local near ring and the ideals of N are totally ordered by inclusion. Also,<br />the symbol valuation $N$-group in near rings has been introduced. Finally, every valuation $N$-group<br />is a valuation near ring.https://jart.guilan.ac.ir/article_5301_c1b24decc85d3c77cfc31b0105f4c715.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39319220211201On some additive mappings on division rings101110530310.22124/jart.2021.19142.1263ENS.AliDepartment of Mathematics,
Faculty of Science,
Aligarh Muslim University, Aligarh, India000-0001-5162-7522A.AbdelwanisDepartment of Mathematics
Faculty of Science
Cairo University
Giza 12613, EgyptJournal Article20210311 Let $D$ be a division ring such that char$(D) \neq 2$ and $\alpha,\beta:D\rightarrow D$ be automorphisms of $D$. The main purpose of this paper is to characterizes additive maps <br />$f$ and $g$ satisfying the identity $f(x)\alpha(x^{-1}) + \beta(x)g(x^{-1}) = 0$ for all $0 \neq x\in D.$ As an application, we describe the structure of an additive map $f$ satisfying the identity <br />$f(x)\alpha(y)+\beta(x)f(y) =l$ for all $x,y\in D$ such that $xy=a,$ where $l,a\in D$ and $a$ is nonzero. With this, many known results can be either generalized or deduced. In particular, we generalized the results proved in<br />\cite{C1} and \cite{C2}, respectively. https://jart.guilan.ac.ir/article_5303_664350d6c417e151b54114b0e421bdfc.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39319220211201Poset properties with respect to semi-ideal based zero-divisor graph111120530410.22124/jart.2021.19454.1268ENBElavarasanDepartment of Mathematics, Karunya Institute of Technology and Sciences,
Coimbatore - 641 114, India.KPorselviDepartment of Mathematics,
Karunya Institute of Technology and Sciences,
Coimbatore - 641 114, Tamilnadu, India.Journal Article20210426In this paper, we discuss some properties of poset $P$ determined by semi-ideal based zero-divisor graph $G_K(P),$ for a semi-ideal $K$ of $P.$ We investigate some interesting properties if $G_K(P)$ contains a cycle. Further, we prove that if $V(G_K(P))$ is a generalized tree, then $(V(G_K(P))\backslash S_x)\cup K$ and $(V(G_K(P))\backslash S_{\geq x})\cup K$ are prime semi-ideals of $P$.https://jart.guilan.ac.ir/article_5304_bcda4b407ce1d80b53f8c29b36bbf837.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39319220211201Generalized Prime Ideal Factorization of Submodules121129530510.22124/jart.2021.19497.1271ENK. R.ThulasiDepartment of Mathematics, Pondicherry University, Puducherry, India.0000-0002-2233-3039T.DuraivelDepartment of Mathematics, Pondicherry University, Puducherry, India.S.MangayarcarassyDepartment of Mathematics, Pondicherry Engineering College, Puducherry, India.Journal Article20210502In this article, we introduce generalized prime ideal factorization for all proper submodules of a finitely generated module over a Noetherian ring. We show that the generalized prime ideal factorization of a product of two coprime ideals is the product of the generalized prime ideal factorization of the ideals. We find conditions under which the generalized prime ideal factorization of a product of prime ideals is equal to the product of the prime ideals. We show that if R is a Dedekind domain, the generalized prime ideal factorization of an ideal I in R is exactly the prime ideal factorization of I.https://jart.guilan.ac.ir/article_5305_206ef4f7e0c845b978892a17192ecc73.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39319220211201On solutions of the Diophantine equation $F_{n_{1}}+F_{n_{2}}+F_{n_{3}}+F_{n_{4}}=2^a$131148532210.22124/jart.2021.19294.1266ENP.TiebekabeDepartment of Mathematics and Computer Science, University
of Cheikh Anta Diop, Dakar, Senegal.0000-0002-1526-0062I.DioufDepartment of Mathematics and Computer Science, University
of Cheikh Anta Diop,, Dakar, Senegal.Journal Article20210405Let $(F_n)_{n\geq 0}$ be the Fibonacci sequence given by $F_0 = 0, F_1 = 1$ and $F_{n+2} = F_{n+1}+F_n$ for $n \geq 0$. In this paper, we solve all powers of two which are sums of four Fibonacci numbers with a few exceptions that we characterize.https://jart.guilan.ac.ir/article_5322_4dbb7688267f38276f282624efaf9151.pdf