Duals of Simple and Subdirectly Irreducible Distributive Modal Algebras

2007 ◽  
pp. 45-57
Author(s):  
Be Birchall
Keyword(s):  
Subdirectly Irreducible ◽  
Modal Algebras

scholarly journals Simple and subdirectly irreducibles bounded distributive lattices with unary operators

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
Sergio Arturo Celani
Keyword(s):  
Distributive Lattices ◽  
Heyting Algebras ◽  
Subdirectly Irreducible ◽  
Modal Algebras ◽  
Heyting Algebras With Operators ◽  
Subdirectly Irreducibles ◽  
Subdirectly Irreducible Algebras

We characterize the simple and subdirectly irreducible distributive algebras in some varieties of distributive lattices with unary operators, including topological and monadic positive modal algebras. Finally, for some varieties of Heyting algebras with operators we apply these results to determine the simple and subdirectly irreducible algebras.

scholarly journals Simple and subdirectly irreducible finitely supported Cb -sets

2018 ◽  
Vol 706 ◽  
pp. 1-21
Author(s):  
M.M. Ebrahimi ◽  
Kh. Keshvardoost ◽  
M. Mahmoudi
Keyword(s):  
Subdirectly Irreducible

SUBDIRECTLY IRREDUCIBLE LEFT SELF DISTRIBUTIVELY GENERATED ALGEBRAS

2001 ◽  
Vol 29 (8) ◽  
pp. 3257-3273 ◽  
Author(s):  
Gary F. Birkenmeier ◽  
Henry E. Heatherly ◽  
John A. Lewallen
Keyword(s):  
Subdirectly Irreducible

scholarly journals Rings whose additive endomorphisms are ring endomorphisms

1990 ◽  
Vol 42 (1) ◽  
pp. 145-152 ◽  
Author(s):  
Gary Birkenmeier ◽  
Henry Heatherly
Keyword(s):  
Subdirectly Irreducible ◽  
Finiteness Conditions ◽  
Chain Conditions ◽  
Open Questions ◽  
Open Case ◽  
Ring Endomorphism ◽  
Substantial Progress ◽  
Additive Endomorphism ◽  
Made In

A ring R is said to be an AE-ring if every additive endomorphism is a ring endomorphism. In this paper further steps are made toward solving Sullivan's Problem of characterising these rings. The classification of AE-rings with. R3 ≠ 0 is completed. Complete characterisations are given for AE-rings which are either: (i) subdirectly irreducible, (ii) algebras over fields, or (iii) additively indecomposable. Substantial progress is made in classifying AE-rings which are mixed – the last open case – by imposing various finiteness conditions (chain conditions on special ideals, height restricting conditions). Several open questions are posed.

An abstract algebraic logic approach to tetravalent modal logics

2000 ◽  
Vol 65 (2) ◽  
pp. 481-518 ◽  
Author(s):  
Josep Maria Font ◽  
Miquel Rius
Keyword(s):  
Algebraic Logic ◽  
Modal Logics ◽  
The Other ◽  
Abstract Algebraic Logic ◽  
Algebraic Semantics ◽  
Modal Algebras ◽  
Logic Approach ◽  
Abstract Logics ◽  
Joint Study

AbstractThis paper contains a joint study of two sentential logics that combine a many-valued character, namely tetravalence, with a modal character; one of them is normal and the other one quasinormal. The method is to study their algebraic counterparts and their abstract models with the tools of Abstract Algebraic Logic, and particularly with those of Brown and Suszko's theory of abstract logics as recently developed by Font and Jansana in their “A General Algebraic Semantics for Sentential Logics”. The logics studied here arise from the algebraic and lattice-theoretical properties we review of Tetravalent Modal Algebras, a class of algebras studied mainly by Loureiro, and also by Figallo. Landini and Ziliani, at the suggestion of the late Antonio Monteiro.

scholarly journals Rings whose proper homomorphic images are right subdirectly irreducible

1974 ◽  
Vol 52 (1) ◽  
pp. 45-51 ◽  
Author(s):  
M. G. Deshpande ◽  
V. Deshpande
Keyword(s):  
Subdirectly Irreducible

σ-Reflexive Semigroups and Rings

1972 ◽  
Vol 15 (2) ◽  
pp. 185-188 ◽  
Author(s):  
M. Chacrono ◽  
G. Thierrin
Keyword(s):  
Commutative Ring ◽  
Subdirectly Irreducible

We shall call a semigroup S a σ-reflexive semigroup if any subsemigroup H in S is reflexive (i.e. for all a, b ∈ S, ab ∈ H implies ba∊H ([2], [5]). It can be verified that any group G is a σ-reflexive semigroup if and only if any subgroup of G is normal. In this paper, we characterize subdirectly irreducible o-reflexive semigroups. We derive the following commutativity result: any generalized commutative ring R ([1]) in which the integers n=n(x, y) in the equation (xy)n = (yx)m can be taken equal to 1 for all x, y ∈ R must be a commutative ring.

Subdirectly Irreducible DQC Rings

1971 ◽  
Vol 14 (4) ◽  
pp. 495-498 ◽  
Author(s):  
W. Burgess ◽  
M. Chacron
Keyword(s):  
Division Ring ◽  
Subdirectly Irreducible ◽  
Simple Ring

AbstractTwenty-five years ago McCoy published a characterization of commutative subdirectly irreducible rings. This result was generalized by Thierrin to duo rings with the word “field” which appeared in McCoy's theorem replaced by “division ring”. The purpose of this note is to give another generalization in which the words “division ring” will be replaced by “simple ring with 1 ”. The techniques resemble those of McCoy and Thierrin.

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