L‐fuzzy congruence classes in universal algebras

2021 ◽  
Author(s):  
Gezahagne Mulat Addis
Keyword(s):  
Universal Algebras ◽  
Fuzzy Congruence ◽  
Congruence Classes

scholarly journals Ideals and other generalizations of congruence classes

1992 ◽  
Vol 53 (1) ◽  
pp. 103-115 ◽  
Author(s):  
Paolo Agliano ◽  
Aldo Ursini
Keyword(s):  
General Context ◽  
Universal Algebras ◽  
Congruence Properties ◽  
Congruence Classes

AbstractIn the general context of ideals in universal algebras, we study varietal properties connected with ideals that are equivalent both to Ma'cev conditions and congruence properties such as 0-regularity, 0-permutability, etc.

Weak Products of Simple Universal Algebras

1969 ◽  
Vol 42 (1-3) ◽  
pp. 157-171 ◽  
Author(s):  
Tah-Kai Hu
Keyword(s):  
Universal Algebras

WHITEHEAD EXACT SEQUENCE AND DIFFERENTIAL GRADED FREE LIE ALGEBRA

2004 ◽  
Vol 15 (10) ◽  
pp. 987-1005 ◽  
Author(s):  
MAHMOUD BENKHALIFA
Keyword(s):  
Exact Sequence ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Integral Domain ◽  
Free Lie Algebra ◽  
Universal Algebras ◽  
Free Lie Algebras ◽  
Equivalent Class

Let R be a principal and integral domain. We say that two differential graded free Lie algebras over R (free dgl for short) are weakly equivalent if and only if the homologies of their corresponding enveloping universal algebras are isomophic. This paper is devoted to the problem of how we can characterize the weakly equivalent class of a free dgl. Our tool to address this question is the Whitehead exact sequence. We show, under a certain condition, that two R-free dgls are weakly equivalent if and only if their Whitehead sequences are isomorphic.

scholarly journals SUMS OF PRODUCTS OF CONGRUENCE CLASSES AND OF ARITHMETIC PROGRESSIONS

2009 ◽  
Vol 05 (04) ◽  
pp. 625-634
Author(s):  
SERGEI V. KONYAGIN ◽  
MELVYN B. NATHANSON
Keyword(s):  
Arithmetic Progression ◽  
Congruence Class ◽  
Arithmetic Progressions ◽  
Sum Of Products ◽  
Sums Of Products ◽  
Positive Integers ◽  
Congruence Classes

Consider the congruence class Rm(a) = {a + im : i ∈ Z} and the infinite arithmetic progression Pm(a) = {a + im : i ∈ N0}. For positive integers a,b,c,d,m the sum of products set Rm(a)Rm(b) + Rm(c)Rm(d) consists of all integers of the form (a+im) · (b+jm)+(c+km)(d+ℓm) for some i,j,k,ℓ ∈ Z. It is proved that if gcd (a,b,c,d,m) = 1, then Rm(a)Rm(b) + Rm(c)Rm(d) is equal to the congruence class Rm(ab+cd), and that the sum of products set Pm(a)Pm(b)+Pm(c)Pm eventually coincides with the infinite arithmetic progression Pm(ab+cd).

scholarly journals Lehmer points and visible points on affine varieties over finite fields

2013 ◽  
Vol 156 (2) ◽  
pp. 193-207 ◽  
Author(s):  
KIT-HO MAK ◽  
ALEXANDRU ZAHARESCU
Keyword(s):  
Finite Fields ◽  
Affine Variety ◽  
Asymptotic Results ◽  
Visible Points ◽  
Congruence Classes

AbstractLet V be an absolutely irreducible affine variety over $\mathbb{F}_p$. A Lehmer point on V is a point whose coordinates satisfy some prescribed congruence conditions, and a visible point is one whose coordinates are relatively prime. Asymptotic results for the number of Lehmer points and visible points on V are obtained, and the distribution of visible points into different congruence classes is investigated.

scholarly journals Congruence Class Sizes in Finite Sectionally Complemented Lattices

2004 ◽  
Vol 47 (2) ◽  
pp. 191-205 ◽  
Author(s):  
G. Grätzer ◽  
E. T. Schmidt
Keyword(s):  
Congruence Class ◽  
Typical Result ◽  
Complemented Lattices ◽  
The Family ◽  
Complemented Lattice ◽  
Congruence Classes

AbstractThe congruences of a finite sectionally complemented lattice L are not necessarily uniform (any two congruence classes of a congruence are of the same size). To measure how far a congruence Θ of L is from being uniform, we introduce Spec Θ, the spectrum of Θ, the family of cardinalities of the congruence classes of Θ. A typical result of this paper characterizes the spectrum S = (mj | j < n) of a nontrivial congruence Θ with the following two properties:

Varieties of infinitary universal algebras

1985 ◽  
Vol 20 (1) ◽  
pp. 123-126
Author(s):  
Ji?� Rosick�
Keyword(s):  
Universal Algebras

Fuzzy congruence pairs of inverse semigroups

1993 ◽  
Vol 56 (1) ◽  
pp. 117-122 ◽  
Author(s):  
Fawzi A. Al-Thukair
Keyword(s):  
Inverse Semigroups ◽  
Fuzzy Congruence
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