强Fregean代数中完全满足不可约同余的结构

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2022-07-13 DOI:10.1007/s00012-022-00787-0

Katarzyna Słomczyńska

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引用次数: 1

摘要

强Fregean代数是这样一个代数，它的同态映象的类是Fregean，并且该代数产生的变种是同余模。为了理解这些代数的结构，我们研究了它们的完全满足不可约同余的偏序集中的素数区间投影关系，并证明了它的陪集具有布尔群的自然结构。特别地，这种方法允许我们将这种代数的同余和元素表示为这些偏序集的上闭子集的子集，这些子集具有一些特殊的性质。

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The structure of completely meet irreducible congruences in strongly Fregean algebras

A strongly Fregean algebra is an algebra such that the class of its homomorphic images is Fregean and the variety generated by this algebra is congruence modular. To understand the structure of these algebras we study the prime intervals projectivity relation in the posets of their completely meet irreducible congruences and show that its cosets have the natural structure of a Boolean group. In particular, this approach allows us to represent congruences and elements of such algebras as the subsets of upward closed subsets of these posets with some special properties.

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来源期刊

Algebra Universalis 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3 months

期刊介绍： Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.