scholarly journals Extensional quotient coalgebras

2017 ◽  
Vol 9 (2) ◽  
pp. 303-323
Author(s):  
Jean-Paul Mavoungou
Keyword(s):  
Congruence Relation ◽  
Maximal Element ◽  
Congruence Relations

Abstract Given an endofunctor F of an arbitrary category, any maximal element of the lattice of congruence relations on an F-coalgebra (A, a) is called a coatomic congruence relation on (A, a). Besides, a coatomic congruence relation K is said to be factor split if the canonical homomor-phism ν : AK → A∇A splits, where ∇A is the largest congruence relation on (A, a). Assuming that F is a covarietor which preserves regular monos, we prove under suitable assumptions on the underlying category that, every quotient coalgebra can be made extensional by taking the regular quotient of an F-coalgebra with respect to a coatomic and not factor split congruence relation or its largest congruence relation.

Congruence relations on almost distributive lattices-II

2019 ◽  
pp. 2150005
Author(s):  
Gezahagne Mulat Addis
Keyword(s):  
Distributive Lattice ◽  
Congruence Relation ◽  
Congruence Class ◽  
Distributive Lattices ◽  
Ideal Formula ◽  
Congruence Relations

For a given ideal [Formula: see text] of an almost distributive lattice [Formula: see text], we study the smallest and the largest congruence relation on [Formula: see text] having [Formula: see text] as a congruence class.

scholarly journals Congruence relations of Ankeny-Artin-Chowla type for pure cubic fields

1984 ◽  
Vol 96 ◽  
pp. 95-112 ◽  
Author(s):  
Hiroshi Ito
Keyword(s):  
Elliptic Curve ◽  
Class Number ◽  
Congruence Relation ◽  
Bernoulli Numbers ◽  
Quadratic Fields ◽  
Hurwitz Numbers ◽  
Real Quadratic Fields ◽  
Congruence Relations ◽  
Cubic Fields ◽  
Real Quadratic

Ankeny, Artin and Chowla [1] proved a congruence relation among the class number, the fundamental unit of real quadratic fields, and the Bernoulli numbers. Our aim of this paper is to prove similar congruence relations for pure cubic fields. For this purpose, we use the Hurwitz numbers associated with the elliptic curve defined by y2 = 4x3 — 1 instead of the Bernoulli numbers (§ 3).

Congruence relations, filters, ideals, and definability in lattices of α-recursively enumerable sets

1976 ◽  
Vol 41 (2) ◽  
pp. 405-418
Author(s):  
Manuel Lerman
Keyword(s):  
Congruence Relation ◽  
Lattice Theory ◽  
Elementary Theory ◽  
Finite Sets ◽  
Recursively Enumerable ◽  
Set Inclusion ◽  
Recursively Enumerable Sets ◽  
Congruence Relations ◽  
Elementary Theories

Throughout this paper, α will denote an admissible ordinal. Let (α) denote the lattice of α-r.e. sets, i.e., the lattice whose elements are the α-r.e. sets, and whose ordering is given by set inclusion. Call a set A ∈ (α)α*-finite if it is α-finite and has ordertype < α* (the Σ1-projectum of α). The α*-finite sets form an ideal of (α), and factoring (α) by this ideal, we obtain the quotient lattice *(α).We will fix a language ℒ suitable for lattice theory, and discuss decidability in terms of this language. Two approaches have succeeded in making some progress towards determining the decidability of the elementary theory of (α). Each approach was first used by Lachlan for α = ω. The first approach is to relate the decidability of the elementary theory of (α) to that of a suitable quotient lattice of (α) by a congruence relation definable in ℒ. This technique was used by Lachlan [4, §1] to obtain the equidecidability of the elementary theories of (ω) and *(ω), and was generalized by us [6, Corollary 1.2] to yield the equidecidability of the elementary theories of (α) and *(α) for all α. Lachlan [3] then adopted a different approach.

scholarly journals Rough sets based on fuzzy ideals in distributive lattices

2020 ◽  
Vol 18 (1) ◽  
pp. 122-137
Author(s):  
Yongwei Yang ◽  
Kuanyun Zhu ◽  
Xiaolong Xin
Keyword(s):  
Distributive Lattice ◽  
Rough Set ◽  
Rough Sets ◽  
Congruence Relation ◽  
Distributive Lattices ◽  
Model Based ◽  
Congruence Relations ◽  
Fuzzy Ideal ◽  
Lower And Upper Approximations ◽  
Generalized Rough Sets

Abstract In this paper, we present a rough set model based on fuzzy ideals of distributive lattices. In fact, we consider a distributive lattice as a universal set and we apply the concept of a fuzzy ideal for definitions of the lower and upper approximations in a distributive lattice. A novel congruence relation induced by a fuzzy ideal of a distributive lattice is introduced. Moreover, we study the special properties of rough sets which can be constructed by means of the congruence relations determined by fuzzy ideals in distributive lattices. Finally, the properties of the generalized rough sets with respect to fuzzy ideals in distributive lattices are also investigated.

scholarly journals Congruence Relations for Shimura Varieties Associated withGU(n–1, 1)

2014 ◽  
Vol 66 (6) ◽  
pp. 1305-1326 ◽  
Author(s):  
Jean-Stefan Koskivirta
Keyword(s):  
Irreducible Component ◽  
Congruence Relation ◽  
Shimura Varieties ◽  
Congruence Relations ◽  
Special Case

AbstractWe prove the congruence relation for the mod–preduction of Shimura varieties associated with a unitary similitude groupGU(n– 1, 1) over ℚ whenpis inert andnodd. The case whennis even was obtained by T. Wedhorn and O. Bültel, as a special case of a result of B. Moonen, when theμ–ordinary locus of thep–isogeny space is dense. This condition fails in our case. We show that every supersingular irreducible component of the special fiber of p–ℐsog is annihilated by a degree one polynomial in the Frobenius elementF, which implies the congruence relation.

Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices

2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Sergio A. Celani
Keyword(s):  
Congruence Relation ◽  
Topological Characterization ◽  
Congruence Relations ◽  
Distributive Semilattices

AbstractIn this paper we shall study a notion of relative annihilator-preserving congruence relation and relative annihilator-preserving homomorphism in the class of bounded distributive semilattices. We shall give a topological characterization of this class of semilattice homomorphisms. We shall prove that the semilattice congruences that are associated with filters are exactly the relative annihilator-preserving congruence relations.

scholarly journals Norms over intuitionistic fuzzy congruence relations on rings

2021 ◽  
Vol 27 (3) ◽  
pp. 51-68
Author(s):  
Rasul Rasuli ◽  
Keyword(s):  
Equivalence Relation ◽  
Congruence Relation ◽  
Equivalence Relations ◽  
Intuitionistic Fuzzy ◽  
Congruence Relations ◽  
Fuzzy Congruence

In this paper, by using norms, we define the concept of intuitionistic fuzzy equivalence relations and intuitionistic fuzzy congruence relations on ring R and we investigate some assertions. Also we define intuitionistic fuzzy ideals of ring R under norms and compare this with fuzzy equivalence relation and fuzzy congruence relation on ring R such that we define new introduced ring.

scholarly journals Compatible Deductive Systems of Pulexes

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Shokoofeh Ghorbani
Keyword(s):  
Congruence Relation ◽  
Deductive System ◽  
Quotient Algebra ◽  
Bijective Correspondence ◽  
Deductive Systems ◽  
Congruence Relations

The notion of (compatible) deductive system of a pulex is defined and some properties of deductive systems are investigated. We also define a congruence relation on a pulex and show that there is a bijective correspondence between the compatible deductive systems and the congruence relations. We define the quotient algebra induced by a compatible deductive system and study its properties.

Extending Algebras to Model Congruence Schemes

1986 ◽  
Vol 38 (2) ◽  
pp. 257-276 ◽  
Author(s):  
J. Berman ◽  
G. Grätzer ◽  
C. R. Platt
Keyword(s):  
Universal Algebra ◽  
Congruence Relation ◽  
Principal Congruence ◽  
Algebraic Functions ◽  
Congruence Relations ◽  
Image Position

This paper is concerned with the description of principal congruence relations. Given elements a and b of a universal algebra , let θ(a, b) denote the smallest congruence relation on containing the pair 〈a, b〉. One of the earliest characterizations of θ(a, b) is Mal'cev's well-known result [5, Theorem 1.10.3], which says that c ≡ d(θ(a, b)) if and only if there exists a sequence z0, z1, …, zn of elements of and a sequence f1, f2, …, fn of unary algebraic functions such that c = z0, d = zn, and for each i = 1, …, n,Although this describes θ(a, b) in terms of a set of unary algebraic functions, it is not possible to predict the number or complexity of the unary functions used independently of the choice of a, b, c and d. Several recent papers ([1], [2], [3], [4], [6]) investigate classes of algebras in which principal congruences are simpler.

scholarly journals Fuzzy Congruence Relations in Generalized Almost Distributive Fuzzy Lattices

2021 ◽  
Vol 2089 (1) ◽  
pp. 012067
Author(s):  
T. Sangeetha ◽  
S. Senthamil Selvi
Keyword(s):  
Prime Ideal ◽  
Congruence Relation ◽  
Subject Classification ◽  
Ams Subject Classification ◽  
Congruence Relations ◽  
Fuzzy Congruence

Abstract This paper defines the fuzzy congruence relation of GADFL (Generalized nearly distributive fuzzy lattices). The ideas of θ - ideal and θ - Prime ideal are introduced in GADFL, and the fuzzy congruence relation is used to explain these ideals. AMS subject classification: 06D72, 06F15, 08A72.

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