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 Filters and congruences in sectionally pseudocomplemented lattices and posets

2021 ◽  
Author(s):  
Ivan Chajda ◽  
Helmut Länger
Keyword(s):  
Algebraic Semantics ◽  
Basic Properties ◽  
Algebraic Constructions ◽  
Pseudocomplemented Lattices ◽  
Intuitionistic Logics

AbstractTogether with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that—similar to relatively pseudocomplemented lattices—these structures can serve as an algebraic semantics of certain intuitionistic logics. The aim of the present paper is to define congruences and filters in these structures, derive mutual relationships between them and describe basic properties of congruences in strongly sectionally pseudocomplemented posets. For the description of filters in both sectionally pseudocomplemented lattices and posets, we use the tools introduced by A. Ursini, i.e., ideal terms and the closedness with respect to them. It seems to be of some interest that a similar machinery can be applied also for strongly sectionally pseudocomplemented posets in spite of the fact that the corresponding ideal terms are not everywhere defined.

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

Sectionally pseudocomplemented lattices and semilattices

2003 ◽  
Author(s):  
I. Chajda ◽  
R. Halaš
Keyword(s):  
Pseudocomplemented Lattices

scholarly journals Bounded endomorphisms of free P-algebras

1992 ◽  
Vol 34 (2) ◽  
pp. 209-214
Author(s):  
Daniel Ševčovič
Keyword(s):  
Free Algebra ◽  
Present Note ◽  
Finitely Generated ◽  
Efficient Tool ◽  
Pseudocomplemented Lattices

The present note deals with bounded endomorphisms of free p-algebras (pseudocomplemented lattices). The idea of bounded homomorphisms was introduced by R. McKenzie in [8]. T. Katriňák [5] subsequently studied the properties of bounded homomorphisms for the varieties of p-algebras. This concept is also an efficient tool for the characterization of, so-called, splitting as well as projective algebras in the varieties of all lattices or p-algebras. For details the reader is referred to [2], [5], [6], [7] and other references therein. Let us emphasize that the main results that are contained in the above mentioned references strongly depend on the boundedness of each endomorphism of any finitely generated free algebra in a given variety.

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
Sign in / Sign up

Export Citation Format

Share Document