Subdirect irreducibility and congruences

1982 ◽  
pp. 256-262
Author(s):  
Aleš Pultr
Keyword(s):  
Subdirect Irreducibility

Subdirect irreducibility and equational compactness in unary algebras

1970 ◽  
Vol 21 (1) ◽  
pp. 256-264 ◽  
Author(s):  
G�nter H. Wenzel
Keyword(s):  
Subdirect Irreducibility ◽  
Equational Compactness

scholarly journals Subdirect irreducibility of algebras and acts with an additional unary operation

2005 ◽  
Vol 6 (2) ◽  
pp. 217 ◽  
Author(s):  
N.V. Loi ◽  
R. Wiegandt
Keyword(s):  
Unary Operation ◽  
Subdirect Irreducibility

scholarly journals Productive classes and subdirect irreducibility, in particular for graphs

1977 ◽  
Vol 20 ◽  
pp. 159-176 ◽  
Author(s):  
A. Pultr ◽  
J. Vinárek
Keyword(s):  
Subdirect Irreducibility

On a common abstraction of de Morgan algebras and Stone algebras

1983 ◽  
Vol 94 (3-4) ◽  
pp. 301-308 ◽  
Author(s):  
T. S. Blyth ◽  
J. C. Varlet
Keyword(s):  
Distributive Lattice ◽  
Subdirectly Irreducible ◽  
Bounded Distributive Lattice ◽  
Subdirect Irreducibility ◽  
De Morgan Algebras ◽  
Simple Equations ◽  
Lattice Of Congruences

SynopsisWe consider a common abstraction of de Morgan algebras and Stone algebras which we call an MS-algebra. The variety of MS-algebras is easily described by adjoining only three simple equations to the axioms for a bounded distributive lattice. We first investigate the elementary properties of these algebras, then we characterise the least congruence which collapses all the elements of an ideal, and those ideals which are congruence kernels. We introduce a congruence which is similar to the Glivenko congruence in a p-algebra and show that the location of this congruence in the lattice of congruences is closely related to the subdirect irreducibility of the algebra. Finally, we give a complete description of the subdirectly irreducible MS-algebras.

scholarly journals GOLDIE DIMENSION, DUAL KRULL DIMENSION AND SUBDIRECT IRREDUCIBILITY

2010 ◽  
Vol 52 (A) ◽  
pp. 19-32 ◽  
Author(s):  
TOMA ALBU
Keyword(s):  
Krull Dimension ◽  
Subdirectly Irreducible ◽  
Modular Lattices ◽  
Survey Paper ◽  
Goldie Dimension ◽  
Subdirect Irreducibility ◽  
Upper Continuous ◽  
Torsion Theories ◽  
Quotient Modules ◽  
Noetherian Modules

AbstractIn this survey paper we present some results relating the Goldie dimension, dual Krull dimension and subdirect irreducibility in modules, torsion theories, Grothendieck categories and lattices. Our interest in studying this topic is rooted in a nice module theoretical result of Carl Faith [Commun. Algebra27 (1999), 1807–1810], characterizing Noetherian modules M by means of the finiteness of the Goldie dimension of all its quotient modules and the ACC on its subdirectly irreducible submodules. Thus, we extend his result in a dual Krull dimension setting and consider its dualization, not only in modules, but also in upper continuous modular lattices, with applications to torsion theories and Grothendieck categories.

A STUDY ON SUBDIRECT IRREDUCIBILITY OF THE SUBGROUP LATTICES OF THE GROUP OF 2×2 MATRICES OVER Z_7

2020 ◽  
Vol 9 (4) ◽  
pp. 1751-1760
Author(s):  
R. Seethalakshmi ◽  
V. D. Murugan ◽  
R. Murugesan
Keyword(s):  
Subdirect Irreducibility ◽  
Subgroup Lattices

scholarly journals A study on subdirect irreducibility of the subgroup lattices of the group of $2 \times 2$ matrices over $Z_3$ and $Z_5$

2020 ◽  
Vol S (1) ◽  
pp. 499-501
Author(s):  
R. Murugesan ◽  
R. Seethalakshmi ◽  
P. Namasivayam
Keyword(s):  
Subdirect Irreducibility ◽  
Subgroup Lattices

Demi-pseudocomplemented lattices: principal congruences and subdirect irreducibility

1990 ◽  
Vol 27 (2) ◽  
pp. 180-193 ◽  
Author(s):  
Hanamantagouda P. Sankappanavar
Keyword(s):  
Subdirect Irreducibility ◽  
Pseudocomplemented Lattices

scholarly journals On subdirect irreducibility and its variants

1982 ◽  
Vol 32 (1) ◽  
pp. 116-121,122-128
Author(s):  
Jiří Vinárek
Keyword(s):  
Subdirect Irreducibility
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