On Fully Closed Stable Modules

Shukur AL-AEASHI; Bijan DAVVAZ

doi:10.48048/wjst.2021.9534

On Fully Closed Stable Modules

Walailak Journal of Science and Technology (WJST) ◽

10.48048/wjst.2021.9534 ◽

2021 ◽

Vol 18 (15) ◽

Author(s):

Shukur AL-AEASHI ◽

Bijan DAVVAZ

Keyword(s):

Multiplication Module ◽

Basic Properties ◽

Algebraic Properties ◽

Stable Module

In this paper, we studied the notion of the fully closed stable module and identified some basic properties of this notion. We also investigated some concepts which are related to this module. In addition, the notion of CL-duo and fully closed stable modules were also studied. HIGHLIGHTS Studying the concept of fully closed stable modules Connect two concepts with important algebraic properties Giving new results to related concepts such as duo module closed multiplication module and closed monomorphism coretractable module

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Fuzzy Normed Rings

Symmetry ◽

10.3390/sym10100515 ◽

2018 ◽

Vol 10 (10) ◽

pp. 515 ◽

Cited By ~ 3

Author(s):

Aykut Emniyet ◽

Memet Şahin

Keyword(s):

Prime Ideal ◽

Fuzzy Sets ◽

Maximal Ideal ◽

Ring Homomorphism ◽

Ring Theory ◽

Basic Properties ◽

Normed Ring ◽

Normed Ideal ◽

Algebraic Properties ◽

Definition Of

In this paper, the concept of fuzzy normed ring is introduced and some basic properties related to it are established. Our definition of normed rings on fuzzy sets leads to a new structure, which we call a fuzzy normed ring. We define fuzzy normed ring homomorphism, fuzzy normed subring, fuzzy normed ideal, fuzzy normed prime ideal, and fuzzy normed maximal ideal of a normed ring, respectively. We show some algebraic properties of normed ring theory on fuzzy sets, prove theorems, and give relevant examples.

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Introduction to AntiGroups

10.54216/ijns.120201 ◽

2020 ◽

pp. 71-80

Author(s):

admin admin ◽

Keyword(s):

Fundamental Theorem ◽

Identity Element ◽

Classical Groups ◽

Basic Properties ◽

Algebraic Properties

The notion of AntiGroups is formally presented in this paper. A particular class of AntiGroups of type-AG[4] is studied with several examples and basic properties presented. In AntiGroups of type-AG[4], the existence of an inverse is taking to be totally false for all the elements while the closure law, the existence of identity element, the axioms of associativity and commutativity are taking to be either partially true, partially indeterminate or partially false for some elements. It is shown that some algebraic properties of the classical groups do not hold in the class of AntiGroups of type-AG[4]. Specifically, it is shown that intersection of two AntiSubgroups is not necessarily an AntiSubgroup and the union of two AntiSubgroups may be an AntiSubgroup. Also, it is shown that distinct left(right) cosets of AntiSubgroups of AntiGroups of type-AG[4] do not partition the AntiGroups; and that Lagranges’ theorem and fundamental theorem of homomorphisms of the classical groups do not hold in the class of AntiGroups of type-AG[4].

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Minimal path cover sets and monomial ideals

Journal of Algebra and Its Applications ◽

10.1142/s0219498815500140 ◽

2014 ◽

Vol 14 (02) ◽

pp. 1550014 ◽

Cited By ~ 3

Author(s):

Leila Sharifan ◽

Mehrdad Nasernejad ◽

Kazem Khashyarmanesh

Keyword(s):

Monomial Ideals ◽

Simple Graph ◽

Minimal Path ◽

Path Cover ◽

Basic Properties ◽

Algebraic Properties

In this paper, we introduce the concepts of minimal path cover sets and the index of covering of a simple graph G, and study the basic properties of these notions. Corresponding to these combinatorial concepts, we define max-path ideal and path cover ideal attached to G and study its algebraic properties in the case that G is a tree. Especially, we characterize the trees in which the max-path ideals have height 1 or 2.

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On Finite and Infinite NeutroRings of Type-NR[8,9]

10.54216/ijns.0110203 ◽

2020 ◽

pp. 87-99

Author(s):

admin admin ◽

Keyword(s):

Fundamental Theorem ◽

Basic Properties ◽

Algebraic Properties ◽

Different Types ◽

Left And Right

NeutroRings are alternatives to the classical rings and they are of different types. NeutroRings in some cases exhibit different algebraic properties, and in some cases they exhibit algebraic properties similar to the classical rings. The objective of this paper is to revisit the concept of NeutroRings and study finite and infinite NeutroRings of type-NR[8,9]. In NeutroRings of type-NR[8,9], the left and right distributive axioms are taking to be either partially true or partially false for some elements; while all other classical laws and axioms are taking to be totally true for all the elements. Several examples and properties of NeutroRings of type-NR[8,9] are presented. NeutroSubrings, NeutroIdeals, NeutroQuotientRings and NeutroRingHomomorphisms of the NeutroRings of type-NR[8,9] are studied with several interesting examples and their basic properties are presented. It is shown that in NeutroRings of type-NR[8,9], the fundamental theorem of homomorphisms of the classical rings holds.

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Some algebraic properties of complex Segre quaternoins

Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine ◽

10.37069/1683-4720-2019-33-13 ◽

2019 ◽

Vol 33 ◽

pp. 158-159

Author(s):

Anatoliy Pogorui ◽

Tamila Kolomiiets

Keyword(s):

Matrix Representation ◽

Complex Numbers ◽

Polynomial Equations ◽

Complex Field ◽

Basic Properties ◽

Algebraic Properties ◽

Cauchy Riemann

This paper deals with the basic properties the algebra of Segre quaternions over the field of complex numbers. We study idempotents, ideals, matrix representation and the Peirce decomposition of this algebra. We also investigate the structure of zeros of a polynomial in Segre complex quaternions by reducing it to the system of four polynomial equations in the complex field. In addition, Cauchy-Riemann type conditions are obtained for the differentiability of a function on the complex Segre quaternionic algebra.

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Operations on Soft Sets Revisited

Journal of Applied Mathematics ◽

10.1155/2013/105752 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 7

Author(s):

Ping Zhu ◽

Qiaoyan Wen

Keyword(s):

Mathematical Tool ◽

Soft Sets ◽

Operation System ◽

Basic Properties ◽

Union Operation ◽

Algebraic Properties

The concept of soft sets introduced by Molodtsov is a general mathematical tool for dealing with uncertainty. Just as the conventional set-theoretic operations of intersection, union, complement, and difference, some corresponding operations on soft sets have been proposed. Unfortunately, such operations cannot keep all classical set-theoretic laws true for soft sets. In this paper, we redefine the intersection, complement, and difference of soft sets and investigate the algebraic properties of these operations along with a known union operation. We find that the new operation system on soft sets inherits all basic properties of operations on classical sets, which justifies our definitions.

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On the Essence and Tipology of International Public Goods

Voprosy Ekonomiki ◽

10.32609/0042-8736-2005-3-131-141 ◽

2005 ◽

pp. 131-141

Author(s):

V. Mortikov

Keyword(s):

Economic Policy ◽

Social Construction ◽

Public Goods ◽

Public Good ◽

Global Public Goods ◽

Club Goods ◽

Basic Properties ◽

International Public Goods ◽

Regional Public Goods ◽

Joint Products

The basic properties of international public goods are analyzed in the paper. Special attention is paid to the typology of international public goods: pure and impure, excludable and nonexcludable, club goods, regional public goods, joint products. The author argues that social construction of international public good depends on many factors, for example, government economic policy. Aggregation technologies in the supply of global public goods are examined.

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