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 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.

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.

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 An investigation on Γ-hypermodules and soft Γ-hypermodules

2021 ◽  
Author(s):  
Sohrab Ostadhadi-dehkordi ◽  
Thomas Vougiouklis ◽  
Bijan Davvaz
Keyword(s):  
Equivalence Relation ◽  
Strongly Regular

Abstract The concept of soft Γ-hypermodules are generalization of soft hypermodules. In this paper, we prove that when the fuzzy Γ-subhypermodule is normal, then equivalence relation μ* defined on Γ-hypermodules are strongly regular and the additive hyperoperation in quotient Γ- hypermodules (fuzzy subhypermodules) are just operations. Also, we prove that all hyperadditions in the quotient Γ-hypermodule induced by normal Γ-subhypermodule are additions.

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 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.

Covariant functor of soft Γ-hyperrings

2018 ◽  
Vol 13 (02) ◽  
pp. 2050037
Author(s):  
S. Ostadhadi-Dehkordi ◽  
K. P. Shum
Keyword(s):  
Equivalence Relation ◽  
Covariant Functor ◽  
Strongly Regular ◽  
Isomorphism Theorems

It is known that a soft [Formula: see text]-hyperring is a generalization of soft ring. The concept of soft [Formula: see text]-hyperring was first introduced by Zhan et al. In fact, Zhan et al. also established three isomorphism theorems of soft rings in 2012. Science then, the study of soft [Formula: see text]-hyperrings has been rapidly grown. The aim of this paper is to consider the equivalence relation on a [Formula: see text]-hyperring previously defined by Zhan et al. It is proved that the above relation is strongly regular and hyperaddition on all quotient soft [Formula: see text]-hyperrings. Also, by using the fundamental relations on [Formula: see text]-hyperrings and hypergroups, we define covariant functor between the category soft [Formula: see text]-hyperrings and soft rings.

Fundamental relations and identities of fuzzy hyperalgebras

2021 ◽  
pp. 1-10
Author(s):  
Narjes Firouzkouhi ◽  
Abbas Amini ◽  
Chun Cheng ◽  
Mehdi Soleymani ◽  
Bijan Davvaz
Keyword(s):  
Universal Algebra ◽  
Equivalence Relation ◽  
Polynomial Function ◽  
Equivalence Relations ◽  
Fundamental Relation ◽  
Term Function ◽  
Biological Phenomena ◽  
Definition Of

Inspired by fuzzy hyperalgebras and fuzzy polynomial function (term function), some homomorphism properties of fundamental relation on fuzzy hyperalgebras are conveyed. The obtained relations of fuzzy hyperalgebra are utilized for certain applications, i.e., biological phenomena and genetics along with some elucidatory examples presenting various aspects of fuzzy hyperalgebras. Then, by considering the definition of identities (weak and strong) as a class of fuzzy polynomial function, the smallest equivalence relation (fundamental relation) is obtained which is an important tool for fuzzy hyperalgebraic systems. Through the characterization of these equivalence relations of a fuzzy hyperalgebra, we assign the smallest equivalence relation α i 1 i 2 ∗ on a fuzzy hyperalgebra via identities where the factor hyperalgebra is a universal algebra. We extend and improve the identities on fuzzy hyperalgebras and characterize the smallest equivalence relation α J ∗ on the set of strong identities.

scholarly journals On Polish groups admitting non-essentially countable actions

2020 ◽  
pp. 1-15
Author(s):  
ALEXANDER S. KECHRIS ◽  
MACIEJ MALICKI ◽  
ARISTOTELIS PANAGIOTOPOULOS ◽  
JOSEPH ZIELINSKI
Keyword(s):  
Equivalence Relation ◽  
Isometry Group ◽  
Alternative Proof ◽  
Orbit Equivalence ◽  
Locally Compact ◽  
Continuous Action ◽  
Polish Groups ◽  
Infinite Dimensional ◽  
Open Question ◽  
New Criterion

Abstract It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. We answer this question positively for the class of all Polish groups that embed in the isometry group of a locally compact metric space. This class contains all non-archimedean Polish groups, for which we provide an alternative proof based on a new criterion for non-essential countability. Finally, we provide the following variant of a theorem of Solecki: every infinite-dimensional Banach space has a continuous action whose orbit equivalence relation is Borel but not essentially countable.

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