Subdirectly irreducible generalized sums of upper semilattice ordered systems of algebras

2002 ◽  
Vol 47 (2) ◽  
pp. 201-211
Author(s):  
J. Płonka ◽  
Z. Szylicka
Keyword(s):  
Subdirectly Irreducible ◽  
Upper Semilattice

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

An α-finite injury method of the unbounded type

1976 ◽  
Vol 41 (1) ◽  
pp. 1-17
Author(s):  
C. T. Chong
Keyword(s):  
Fine Structure ◽  
Initial Segment ◽  
Fundamental Importance ◽  
Upper Semilattice ◽  
The Past ◽  
Recursively Enumerable ◽  
Background Material ◽  
A Priority ◽  
Admissible Ordinals ◽  
Priority Argument

Let α be an admissible ordinal. In this paper we study the structure of the upper semilattice of α-recursively enumerable degrees. Various results about the structure which are of fundamental importance had been obtained during the past two years (Sacks-Simpson [7], Lerman [4], Shore [9]). In particular, the method of finite priority argument of Friedberg and Muchnik was successfully generalized in [7] to an α-finite priority argument to give a solution of Post's problem for all admissible ordinals. We refer the reader to [7] for background material, and we also follow closely the notations used there.Whereas [7] and [4] study priority arguments in which the number of injuries inflicted on a proper initial segment of requirements can be effectively bounded (Lemma 2.3 of [7]), we tackle here priority arguments in which no such bounds exist. To this end, we focus our attention on the fine structure of Lα, much in the fashion of Jensen [2], and show that we can still use a priority argument on an indexing set of requirements just short enough to give us the necessary bounds we seek.

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.

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.

On Finitely Generated Lattices of Finite Width

1981 ◽  
Vol 33 (1) ◽  
pp. 28-48 ◽  
Author(s):  
W. Poguntke ◽  
B. Sands
Keyword(s):  
Finite Width ◽  
Subdirectly Irreducible ◽  
Finitely Generated ◽  
Simple Lattice ◽  
Irreducible Lattice ◽  
Made In

The width of a lattice L is the maximum number of pairwise noncomparable elements in L.It has been known for some time ([5] ; see also [4]) that there is just one subdirectly irreducible lattice of width twro, namely the five-element nonmodular lattice N5. It follows that every lattice of width two is in the variety of N5, and that every finitely generated lattice of width two is finite.Beginning a study of lattices of width three, W. Poguntke [6] showed that there are infinitely many finite simple lattices of width three. Further studies on width three lattices were made in [3], where it was asked whether every finitely generated simple lattice of width three is finite. In this paper we will show that, in fact, more is true:THEOREM 1.1. Every finitely generated subdirectly irreducible lattice of width three is finite.

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