scholarly journals A Comparison of Complete Parts on m-Idempotent Hyperrings

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 554
Author(s):  
Azam Adineh Zadeh ◽  
Morteza Norouzi ◽  
Irina Cristea
Keyword(s):  
Equivalence Relation ◽  
Quotient Ring ◽  
Transitivity Property ◽  
Strongly Regular ◽  
Regular Equivalence ◽  
Symmetrical Group

On a particular class of m-idempotent hyperrings, the relation ξ m * is the smallest strongly regular equivalence such that the related quotient ring is commutative. Thus, on such hyperrings, ξ m * is a new representation for the α * -relation. In this paper, the ξ m -parts on hyperrings are defined and compared with complete parts, α -parts, and m-complete parts, as generalizations of complete parts in hyperrings. It is also shown how the ξ m -parts help us to study the transitivity property of the ξ m -relation. Finally, ξ m -complete hyperrings are introduced and studied, stressing on the fact that they can be characterized by ξ m -parts. The symmetry plays a fundamental role in this study, since the protagonist is an equivalence relation, defined using also the symmetrical group of permutations of order n.

scholarly journals Transitivity of the εm-relation on (m-idempotent) hyperrings

2018 ◽  
Vol 16 (1) ◽  
pp. 1012-1021 ◽  
Author(s):  
Morteza Norouzi ◽  
Irina Cristea
Keyword(s):  
Equivalence Relation ◽  
Transitive Closure ◽  
Fundamental Relation ◽  
Strongly Regular ◽  
Regular Equivalence ◽  
Quotient Set ◽  
Classical Ring

AbstractOn a general hyperring, there is a fundamental relation, denoted γ*, such that the quotient set is a classical ring. In a previous paper, the authors defined the relation εm on general hyperrings, proving that its transitive closure $\begin{array}{} \displaystyle \varepsilon^{*}_{m} \end{array}$ is a strongly regular equivalence relation smaller than the γ*-relation on some classes of hyperrings, such that the associated quotient structure modulo $\begin{array}{} \displaystyle \varepsilon^{*}_{m} \end{array}$ is an ordinary ring. Thus, on such hyperrings, $\begin{array}{} \displaystyle \varepsilon^{*}_{m} \end{array}$ is a fundamental relation. In this paper, we discuss the transitivity conditions of the εm-relation on hyperrings and m-idempotent hyperrings.

Γ∗-Relation on Fuzzy Hyperrings and Fundamental Ring

2021 ◽  
pp. 1-11
Author(s):  
N. Firouzkouhi ◽  
B. Davvaz
Keyword(s):  
Universal Algebra ◽  
Equivalence Relation ◽  
Fundamental Relation ◽  
Complete Part ◽  
Strongly Regular ◽  
Regular Equivalence ◽  
Fundamental Ring ◽  
Algebraic Hyperstructure

Fundamental relation performs an important role on fuzzy algebraic hyperstructure and is considered as the smallest equivalence relation such that the quotient is a universal algebra. In this paper, we introduce a new fuzzy strongly regular equivalence on fuzzy hyperrings such that the set of the quotient is a ring that is non-commutative. Also, we introduce the concept of a complete part of a fuzzy hyperring and study its principal traits. At last, we convey the relevance between the fundamental relation and complete parts of a fuzzy hyperring.

scholarly journals Cyclic Groups Obtained as Quotient Hypergroups

2015 ◽  
Vol 61 (1) ◽  
pp. 109-122
Author(s):  
S.Sh. Mousavi ◽  
V. Leoreanu-Fotea ◽  
M. Jafarpour
Keyword(s):  
Cyclic Group ◽  
Equivalence Relation ◽  
Cyclic Groups ◽  
Strongly Regular ◽  
Regular Equivalence ◽  
Transitivity Condition

Abstract We introduce a strongly regular equivalence relation ρ*A on the hypergroup H, such that in a particular case the quotient is a cyclic group. Then by using the notion of ρ*A-parts, we investigate the transitivity condition of ρA. Finally, a characterization of the derived hypergroup Dc(H) has been considered.

scholarly journals Generalized fuzzy hypergraphs and hypergroupoids

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2375-2387 ◽  
Author(s):  
Mahdi Farshi ◽  
Bijan Davvaz
Keyword(s):  
Equivalence Relation ◽  
Higher Order ◽  
Regular Equivalence ◽  
Fuzzy Hypergraphs

This article first generalizes the ordinary fuzzy hypergraphs to generalized fuzzy hypergraphs and it makes a connection between generalized fuzzy hypergraphs and fuzzy hyperstructures. We construct a partial fuzzy hypergroupoid associated with it, giving some properties of the associated fuzzy hyperstructure. Moreover, we construct higher order fuzzy hypergroupoids and study their properties. Finally, by considering a regular equivalence relation on a (g-f)p-hypergroupoid, we define a quotient (g-f)phypergroupoid and we investigate some relationships between diagonal product of hypergroupoids and p-product of (g-f)-hypergraphs.

scholarly journals Quotient rings of semiprime rings with bounded index

1982 ◽  
Vol 23 (1) ◽  
pp. 53-64 ◽  
Author(s):  
John Hannah
Keyword(s):  
Direct Product ◽  
Polynomial Identity ◽  
Semiprime Ring ◽  
Quotient Ring ◽  
Matrix Rings ◽  
Special Cases ◽  
Semiprime Rings ◽  
Strongly Regular ◽  
Quotient Rings ◽  
Finite Direct Product

We say that a ring R has bounded index if there is a positive integer n such that an = 0 for each nilpotent element a of R. If n is the least such integer we say R has index n. For example, any semiprime right Goldie ring has bounded index, and so does any semiprime ring satisfying a polynomial identity [10, Theorem 10.8.2]. This paper is mainly concerned with the maximal (right) quotient ring Q of a semiprime ring R with bounded index. Several special cases of this situation have already received attention in the literature. If R satisfies a polynomial identity [1], or if every nonzero right ideal of R contains a nonzero idempotent [18] then it is known that Q is a finite direct product of matrix rings over strongly regular self-injective rings, the size of the matrices being bounded by the index of R. On the other hand if R is reduced (that is, has index 1) then Q is a direct product of a strongly regular self-injective ring and a biregular right self-injective ring of type III ([2] and [15]; the terminology is explained in [6]). We prove the following generalization of these results (see Theorems 9 and 11).

Solvable groups derived from hypergroups

2016 ◽  
Vol 15 (04) ◽  
pp. 1650067 ◽  
Author(s):  
M. Jafarpour ◽  
H. Aghabozorgi ◽  
B. Davvaz
Keyword(s):  
Solvable Group ◽  
Equivalence Relation ◽  
Solvable Groups ◽  
Equivalence Classes ◽  
Strongly Regular

In this paper, we introduce the smallest equivalence relation [Formula: see text] on a hypergroup [Formula: see text] such that the quotient [Formula: see text], the set of all equivalence classes, is a solvable group. The characterization of solvable groups via strongly regular relations is investigated and several results on the topic are presented.

scholarly journals A further study on ordered regular equivalence relations in ordered semihypergroups

2018 ◽  
Vol 16 (1) ◽  
pp. 168-184 ◽  
Author(s):  
Jian Tang ◽  
Xinyang Feng ◽  
Bijan Davvaz ◽  
Xiang-Yun Xie
Keyword(s):  
Equivalence Relation ◽  
Open Problem ◽  
Equivalence Relations ◽  
Ordered Semigroups ◽  
Regular Equivalence

AbstractIn this paper, we study the ordered regular equivalence relations on ordered semihypergroups in detail. To begin with, we introduce the concept of weak pseudoorders on an ordered semihypergroup, and investigate several related properties. In particular, we construct an ordered regular equivalence relation on an ordered semihypergroup by a weak pseudoorder. As an application of the above result, we completely solve the open problem on ordered semihypergroups introduced in [B. Davvaz, P. Corsini and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseuoorders, European J. Combinatorics 44 (2015), 208–217]. Furthermore, we establish the relationships between ordered regular equivalence relations and weak pseudoorders on an ordered semihypergroup, and give some homomorphism theorems of ordered semihypergroups, which are generalizations of similar results in ordered semigroups.

scholarly journals GENERICALLY STABLE REGULAR TYPES

2015 ◽  
Vol 80 (1) ◽  
pp. 308-321 ◽  
Author(s):  
PREDRAG TANOVIĆ
Keyword(s):  
Equivalence Relation ◽  
Generic Stability ◽  
Strongly Regular

AbstractWe study nonorthogonality of symmetric, regular types and show that it preserves generic stability and is an equivalence relation on the set of all generically stable, regular types. We prove that some of the nice properties from the stable context hold in general. In the case of strongly regular types we will relate to the global Rudin–Keisler order.

scholarly journals Factor multialgebras, universal algebras and fuzzy sets

2015 ◽  
Vol 31 (1) ◽  
pp. 111-118
Author(s):  
COSMIN PELEA ◽  
◽  
IOAN PURDEA ◽  
LIANA STANCA ◽  
◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Equivalence Relations ◽  
Universal Algebras ◽  
General Investigation ◽  
Strongly Regular ◽  
Regular Equivalence

Our general investigation of universal algebras obtained from multialgebras via strongly regular equivalence relations provides useful general results concerning fuzzy set topics related to multialgebra theory. We also give many hints on how to connect our approach with the results from the literature.

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