Yazd UniversityAlgebraic Structures and Their Applications2382-97619220220809$\Lambda$-Extension of binary matroids110260810.22034/as.2022.2608ENMortezaKazemzadehDepartment of mathematics, Urmia University, Urmia, IranHabibAzanchilerDepartment of Mathematics, Urmia University, Urmia, IranVahidGhorbaniDepartment of mathematics, Urmia University, Urmia, Iran0000-0002-7301-6973Journal Article20201123In 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.https://as.yazd.ac.ir/article_2608_f53a9300008415032ffbb8107eb4a991.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619220220809GE-derivations1135263110.22034/as.2022.2631ENYoung BaeJunDepartment of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea.0000-0002-0181-8969RavikumarBandaruDepartment of Mathematics, GITAM,
Hyderabad Campus, Telangana-502329, India.0000-0001-8661-7914Journal Article20220103The 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.https://as.yazd.ac.ir/article_2631_19b2d0cde0181374b2f00305f9e16fc7.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619220220809Some separation axioms in topoframes3756265310.22034/as.2022.2653ENMohammadZarghaniFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, IranAli AkbarEstajiFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran0000-0001-8993-5109AbolghasemKarimi FeizabadiDepartment of Mathematics,
Islamic Azad University (Gorgan Branch),
Gorgan,
Iran0000-0002-5659-8262Journal Article20210615This 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.https://as.yazd.ac.ir/article_2653_af772d559885d6f74d6c2e95e7c4c0c1.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619220220809Characterization of monoids by a generalization of weak flatness property5775265510.22034/as.2022.2655ENMahdiyehAbbasiDepartment of Mathematics, Zahedan Branch, Islamic Azad University, Zahedan, Iran0000000348482021HosseinMohammadzadeh SaanyDepartment of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran0000-0002-3833-5821Journal Article20210622In [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.https://as.yazd.ac.ir/article_2655_557e8ba36783dc32a757b7733ad36f77.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619220220809Binary block-codes of $MV$-algebras and Fibonacci sequences7795267110.22034/as.2022.2671ENMortezaAfshar JahanshahiDepartment of Mathematics, Faculty of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, Iran.ArshamBorumand SaeidDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran0000-0001-9495-6027Journal Article20220206In 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.https://as.yazd.ac.ir/article_2671_44948bbdbe7d58687905a00c5abfc0b8.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619220220809On the essential $CP$-spaces97111267410.22034/as.2022.2674ENSahamMajidipourDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranRostamMohamadianDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran0000-0003-3350-366XMehrdadNamdariDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran0000-0003-0966-7234SomayehSoltanpourDepartment of Science, Ahvaz Faculty of Petroleum, Petroleum University of Technology, Ahvaz, Iran0000-0002-1072-9845Journal Article20220208Let $C_c(X)$ 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.https://as.yazd.ac.ir/article_2674_c6eab8768fd228c71acb7067a118ac93.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619220220809A 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 order113120267510.22034/as.2022.2675ENBehnamEbrahimzadehDepartment of Mathematics, Persian Gulf University, Bushehr, Iran0000-0001-5696-275xAliIranmaneshDepartment of Mathematics, Tarbiat Modares University, Tehran, Iran0000-0003-2639-9454Journal Article20210922In 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.https://as.yazd.ac.ir/article_2675_609f365e23655404c49e8672ef7ade41.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619220220809Modules whose surjective endomorphisms have a $\gamma$-small kernels121133267710.22034/as.2022.2677ENAbderrahimEl MoussaouyDepartment of Mathematics, Faculty of Sciences, University of Mohammed First, Oujda, Morocco0000-0001-9630-4698M'HammedZianeDepartment of Mathematics, Faculty of Sciences, University of Mohammed First, Oujda, Morocco.Journal Article20201021In 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.https://as.yazd.ac.ir/article_2677_ce8f00f2599e8515904ded9597a85ec7.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619220220809r-notion of Conjugacy in Partial and Full Injective Transformations135148269310.22034/as.2022.2667ENAftab HussainShahDepartment of Mathematics, Central University of Kashmir, Ganderbal, 191201.Mohd RafiqParrayDepartment of Mathematics, Central University of Kashmir, Ganderbal, 191201.Journal Article20220119In 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.https://as.yazd.ac.ir/article_2693_e32d6799b50cbfcde90d2bc7fc0fe335.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619220220809Characterizations of $J$-prime ideals and $M_{J}$-ideals in posets149162271910.22034/as.2022.2719ENJCatherine Grace JohnDepartment of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore-641114, Tamilnadu, India.0000-0002-3352-3436BElavarasanDepartment of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore-641114, Tamilnadu, India.0000-0002-1414-2814Journal Article20220110In 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 $\mathcal{P}$.https://as.yazd.ac.ir/article_2719_a2762fdd9d71cb0959128b045bc4dc4f.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619220220809A note on $\sigma$-ideals of distributive lattices163179272010.22034/as.2022.2720ENMukkamalaSambasiva RaoDepartment of Mathematics, MVGR College of Engineering, Vizianagaram, Andhra Pradesh, India-5350050000-0002-1627-9603Journal Article20220102Some 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.https://as.yazd.ac.ir/article_2720_805ecd24baee577adeb94b5b3357d8da.pdfYazd UniversityAlgebraic Structures and Their Applications2382-97619220220809Some Remarks on $(\operatorname{INC}(R))^{c}$181198272810.22034/as.2022.2728ENKrishna LPurohitDepartment of Applied Sciences, RK University, Rajkot-360020, Gujarat, India.0000-0003-0164-4425JaydeepParejiyaDepartment of Mathematics, Government Polytechnic, Rajkot-360003, Gujarat, India.Mahesh MParsaniaDepartment of Applied Sciences, RK University, Rajkot-360020, Gujarat, India.Journal Article20220602Let $R$ be a commutative ring with identity $1 \neq 0$ which admits atleast 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 $(\operatorname{INC}(R))^{c}$.https://as.yazd.ac.ir/article_2728_f39a6f6a24600b29ee4c547dbc9f4923.pdf