On finite algebras having a linear congruence class geometry

1984 ◽  
Vol 19 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Thomas Ihringer
Keyword(s):  
Congruence Class ◽  
Linear Congruence ◽  
Finite Algebras ◽  
Class Geometry

On groupoids having a linear congruence class geometry

1982 ◽  
Vol 180 (2) ◽  
pp. 395-411 ◽  
Author(s):  
Thomas Ihringer
Keyword(s):  
Congruence Class ◽  
Linear Congruence ◽  
Class Geometry

scholarly journals RSA Cryptography Algorithm Using linear Congruence Class.

2016 ◽  
Vol 4 (5) ◽  
pp. 1335-1347
Author(s):  
PurnaChandra Sethi ◽  
◽  
PrafullaKumar Behera ◽  
Keyword(s):  
Congruence Class ◽  
Linear Congruence ◽  
Rsa Cryptography

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 Identities in finite algebras

1954 ◽  
Vol 5 (1) ◽  
pp. 8-8 ◽  
Author(s):  
R. C. Lyndon
Keyword(s):  
Finite Algebras

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 On representing Mn's by congruence lattice of finite algebras

1983 ◽  
Vol 44 (3) ◽  
pp. 299-308 ◽  
Author(s):  
M.G. Stone ◽  
R.H. Weedmark
Keyword(s):  
Congruence Lattice ◽  
Finite Algebras

On Pseudovarieties of Forest Algebras

2016 ◽  
Vol 27 (08) ◽  
pp. 909-941 ◽  
Author(s):  
Saeid Alirezazadeh
Keyword(s):  
Natural Extension ◽  
Direct Products ◽  
Property A ◽  
Residually Finite ◽  
Finite Algebras

Forest algebras are defined for investigating languages of forests [ordered sequences] of unranked trees, where a node may have more than two [ordered] successors. They consist of two monoids, the horizontal and the vertical, with an action of the vertical monoid on the horizontal monoid, and a complementary axiom of faithfulness. In the study of forest algebras one of the main difficulties is how to handle the faithfulness property. A pseudovariety is a class of finite algebras of a given signature, closed under the taking of homomorphic images, subalgebras and finitary direct products. We tried to adapt in this context some of the results in the theory of semigroups, specially the studies on relatively free profinite semigroups, which are an important tool in the theory of pseudovarieties of semigroups. We define a new version of syntactic congruence of a subset of the free forest algebra, not just a forest language. This new version is the natural extension of the syntactic congruence for monoids in the case of forest algebras and is used in the proof of an analog of Hunter’s Lemma. We show that under a certain assumption the two versions of syntactic congruences coincide. We adapt some results of Almeida on metric semigroups to the context of forest algebras. We show that the analog of Hunter’s Lemma holds for metric forest algebras, which leads to the result that zero-dimensional compact metric forest algebras are residually finite. We show an analog of Reiterman’s Theorem, which is based on a study of the structure profinite forest algebras.

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:

scholarly journals DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS

2014 ◽  
Vol 57 (3) ◽  
pp. 693-707
Author(s):  
YEMON CHOI
Keyword(s):  
Invertible Element ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Complex Line ◽  
Locally Compact ◽  
The Real ◽  
C Algebra ◽  
Finite Algebras ◽  
Unimodular Group ◽  
Reduced Group

AbstractAn algebraAis said to be directly finite if each left-invertible element in the (conditional) unitization ofAis right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras ofp-pseudofunctions, showing that these algebras are directly finite ifGis amenable and unimodular, or unimodular with the Kunze–Stein property. An exposition is also given of how existing results from the literature imply thatL1(G) is not directly finite whenGis the affine group of either the real or complex line.

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