scholarly journals SOME REGULAR EQUIVALENCE RELATION ON THE SEMIHYPERGROUP OF THE PARTIAL TRANSFORMATION SEMIGROUP ON A SET AND LOCAL SUBSEMIHYPERGROUPS WITH THAT REGULAR EQUIVALENCE RELATION

2015 ◽  
Vol 101 (1) ◽  
Author(s):  
R.I. Sararnrakskul ◽  
S. Pianskool
Keyword(s):  
Equivalence Relation ◽  
Transformation Semigroup ◽  
Partial Transformation ◽  
Regular Equivalence

scholarly journals On Magnifying Elements in E-Preserving Partial Transformation Semigroups

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 160
Author(s):  
Thananya Kaewnoi ◽  
Montakarn Petapirak ◽  
Ronnason Chinram
Keyword(s):  
Equivalence Relation ◽  
Transformation Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Proper Subset ◽  
Partial Transformation ◽  
Transformation Semigroups ◽  
Necessary And Sufficient

Let S be a semigroup. An element a of S is called a right [left] magnifying element if there exists a proper subset M of S satisfying S = M a [ S = a M ] . Let E be an equivalence relation on a nonempty set X. In this paper, we consider the semigroup P ( X , E ) consisting of all E-preserving partial transformations, which is a subsemigroup of the partial transformation semigroup P ( X ) . The main propose of this paper is to show the necessary and sufficient conditions for elements in P ( X , E ) to be right or left magnifying.

Naturally Ordered Transformation Semigroups Preserving an Equivalence Relation and a Cross-section

2011 ◽  
Vol 18 (03) ◽  
pp. 523-532 ◽  
Author(s):  
Lei Sun ◽  
Weina Deng ◽  
Huisheng Pei
Keyword(s):  
Cross Section ◽  
Equivalence Relation ◽  
Transformation Semigroup ◽  
Natural Order ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Minimal Elements ◽  
Full Transformation Semigroup

The paper is concerned with the so-called natural order on the semigroup [Formula: see text], where [Formula: see text] is the full transformation semigroup on a set X, E is a non-trivial equivalence on X and R is a cross-section of the partition X/E induced by E. We determine when two elements of TE(X,R) are related under this order, find elements of TE(X,R) which are compatible with ≤ on TE(X,R), and observe the maximal and minimal elements and the covering elements.

scholarly journals On theS-Invariance Property forS-Flows

2010 ◽  
Vol 2010 ◽  
pp. 1-5
Author(s):  
Amin Saif ◽  
Adem Kılıçman
Keyword(s):  
Topological Space ◽  
Equivalence Relation ◽  
Transformation Semigroup ◽  
Invariance Property ◽  
Topological Monoid

We define an equivalence relation on a topological space which is acted by topological monoidSas a transformation semigroup. Then, we give some results about theS-invariant classes for this relation. We also provide a condition for the existence of relativeS-invariant classes.

A PARTIAL ORDER ON TRANSFORMATION SEMIGROUPS THAT PRESERVE DOUBLE DIRECTION EQUIVALENCE RELATION

2013 ◽  
Vol 12 (08) ◽  
pp. 1350041 ◽  
Author(s):  
LEI SUN ◽  
JUNLING SUN
Keyword(s):  
Lower Bound ◽  
Partial Order ◽  
Equivalence Relation ◽  
Transformation Semigroup ◽  
Natural Partial Order ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Minimal Elements ◽  
Full Transformation Semigroup

Let [Formula: see text] be the full transformation semigroup on a nonempty set X and E be an equivalence relation on X. Then [Formula: see text] is a subsemigroup of [Formula: see text]. In this paper, we endow it with the natural partial order. With respect to this partial order, we determine when two elements are related, find the elements which are compatible and describe the maximal (minimal) elements. Also, we investigate the greatest lower bound of two elements.

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 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.

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.

On some semigroups of the partial transformation semigroup

2012 ◽  
Author(s):  
Ivan D. Trendafilov ◽  
Dimitrinka I. Vladeva
Keyword(s):  
Transformation Semigroup ◽  
Partial Transformation

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.

Abundant Semigroups of Transformations Preserving an Equivalence Relation

2011 ◽  
Vol 18 (01) ◽  
pp. 77-82 ◽  
Author(s):  
Huisheng Pei ◽  
Huijuan Zhou
Keyword(s):  
Equivalence Relation ◽  
Transformation Semigroup ◽  
Equivalence Relations ◽  
Full Transformation ◽  
Full Transformation Semigroup ◽  
Abundant Semigroups

Let X be a set with |X| ≥ 3, [Formula: see text] the full transformation semigroup on X, and E an equivalence relation on X. Let TE(X) be the set of transformations f in [Formula: see text] which preserve E, i.e., (x,y) ∈ E implies (f(x),f(y)) ∈ E. It is known that TE(X) is a subsemigroup of [Formula: see text]. In this paper, we describe the equivalence relations E so that the semigroup TE(X) is abundant.

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