含有满足不可约同余格的子代数的一元代数

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2022-08-05 DOI:10.1007/s00012-022-00786-1

Lucia Janičková

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引用次数: 1

摘要

具有固定基集A的所有代数的所有同余格的系统形成关于包含的格，表示为\（\mathcal{E}_A\)。设A是有限的。\（\mathcal）的满足不可约元素{E}_A\)是一元代数的同余格。我们假设（A，f）有一个连通子代数B，使得B包含至少3个循环元素，并且在\（｛\mathcal｛E｝｝_B\）中满足不可约，并且我们证明了\（｛｛\，\mathrm｛Con｝，｝）在\（{\mathcal{E｝}_A\）中符合不可约的几个充分条件。

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Monounary algebras containing subalgebras with meet-irreducible congruence lattice

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Monounary algebras containing subalgebras with meet-irreducible congruence lattice

The system of all congruence lattices of all algebras with fixed base set A forms a lattice with respect to inclusion, denoted by \(\mathcal {E}_A\). Let A be finite. The meet-irreducible elements of \(\mathcal {E}_A\) are congruence lattices of monounary algebras. We assume that (A, f) has a connected subalgebra B such that B contains at least 3 cyclic elements and is meet-irreducible in \({\mathcal {E}}_B\) and we prove several sufficient conditions under which \({{\,\mathrm{Con}\,}}(A, f)\) is meet-irreducible in \({\mathcal {E}}_A\).

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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.