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

Alexander Abian. On the solvability of infinite systems of Boolean polynomial equations. Colloquium mathematicum, vol. 21 (1970), pp. 27–30. - Alexander Abian. Generalized completeness theorem and solvability of systems of Boolean polynomial equations. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 16 (1970), pp. 263–264. - Paul D. Bacsich. Injectivity in model theory. Colloquium mathematicum, vol. 25 (1972), pp. 165–176. - S. Bulman-Fleming. On equationally compact semilattices. Algebra universalis (Basel), vol. 2 no. 2 (1972), pp. 146–151. - G. Grätzer and H. Lakser. Equationally compact semilattices. Colloquium mathematicum, vol. 20 (1969), pp. 27–30. - David K. Haley. On compact commutative Noetherian rings. Mathematische Annalen, vol. 189 (1970), pp. 272–274. - Ralph McKenzie. ℵ1-incompactness of Z. Colloquium mathematicum, vol. 23 (1971), pp. 199–202. - Jan Mycielski. Some compactifications of general algebras. Colloquium mathematicum, vol. 13 no. 1 (1964), pp. 1–9. See Errata on page 281 of next paper. - Jan Mycielski and C. Ryll-Nardzewski. Equationally compact algebras II. Fundamenta mathematicae, vol. 61 (1968), pp. 271–281. Errata, Fundamenta mathematicae, vol. 62 (1968), p. 309. - L. Pacholski and B. Wȩglorz. Topologically compact structures and positive formulas. Colloquium mathematicum, vol. 19 (1968), pp. 37–42. - B. Wȩglorz. Compactness of algebraic systems. Bulletin de l'Academie Polonaise des Sciences, Série des sciences mathématiques, astronomiques et physiques, vol. 13 (1965), pp. 705–706. - B. Wȩglorz. Equationally compact algebras(I). Fundamenta mathematicae, vol. 59 (1966), pp. 289–298. - B. Wȩglorz. Equationally compact algebras (III). Fundamenta mathematicae, vol. 60 (1967), pp. 89–93. - B. Wȩglorz. Completeness and compactness of lattices. Colloquium mathematicum, vol. 16 (1967), pp. 243–248. - B. Wȩglorz and A. Wojciechowska. Summability of pure extensions of relational structures. Colloquium mathematicum, vol. 19 (1968), pp. 27–35. - Günter H. Wenzel. Subdirect irreducibility and equational compactness of unary algebras 〈A; f〉. Archiv der Mathematik, vol. 21 (1970), pp. 256–264. - Günter H. Wenzel. On -atomic compact relational systems. Mathematische Annalen, vol. 194 (1971), pp. 12–18.

1975 ◽  
Vol 40 (1) ◽  
pp. 88-92 ◽  
Author(s):  
Walter Taylor
Keyword(s):  
Model Theory ◽  
Completeness Theorem ◽  
Noetherian Rings ◽  
Polynomial Equations ◽  
Algebraic Systems ◽  
Relational Structures ◽  
Infinite Systems ◽  
Subdirect Irreducibility ◽  
Relational Systems ◽  
Equational Compactness

scholarly journals Equational compactness in infinitary algebras

1973 ◽  
Vol 27 (2) ◽  
pp. 197-205 ◽  
Author(s):  
Bernhard Banaschewski ◽  
Evelyn Nelson
Keyword(s):  
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

Infinitary equational compactness

1974 ◽  
Vol 4 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Evelyn Nelson
Keyword(s):  
Equational Compactness

Equational compactness of sheaves of algebras on a Noetherian locale

1983 ◽  
Vol 16 (1) ◽  
pp. 318-330 ◽  
Author(s):  
M. Mehdi Ebrahimi
Keyword(s):  
Equational Compactness

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.

Small congruence distributive varieties: Retracts, injectives, equational compactness and amalgamation

1996 ◽  
Vol 33 (3) ◽  
pp. 207-228 ◽  
Author(s):  
P. Ouwehand ◽  
H. Rose
Keyword(s):  
Small Congruence ◽  
Equational Compactness ◽  
Congruence Distributive

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.

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