Meet infinite distributivity for congruence lattices of direct sums of algebras-Reference-Cited by-同舟云学术

Meet infinite distributivity for congruence lattices of direct sums of algebras

Published:2022-03-28 Issue:2 Volume:72 Page:333-340
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Ghumashyan Heghine¹²,Guričan Jaroslav³

Affiliation:

1. Faculty of Information Technology, European University , Yerevan , Armenia

2. Comenius University Bratislava , Bratislava , Slovakia

3. Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava , Bratislava , Slovakia

Abstract

Abstract We study meet infinite distributivity (MID) in congruence lattices of direct sums of algebras. The main result of this note is that in a congruence distributive variety the MID of congruence lattices is preserved by direct sums of algebras, it means that the congruence lattice of a direct sum of algebras is MID if and only if a congruence lattice of every constituent algebra is MID.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2022-0022/pdf

Reference9 articles.

1. Blyth, T. S.—Fang, J.—Silva, H. J.: The endomorphism kernel property in finite distributive lattices and de Morgan algebras, Comm. Algebra 32(6) (2004), 2225–2242.

2. Fang, J.—Sun, Z.-J.: Finite abelian groups with the strong endomorphism kernel property, Acta Math. Sin. (Engl. Ser.) 36(9) (2020), 1076–1082.

3. Fraser, G. A.—Horn, A.: Congruence relations in direct products, Proc. Amer. Math. Soc. 26 (1970), 390–394.

4. Grätzer, G.: Lattice Theory: Foundation, Birkhäuser, Basel, 2011.

5. Ghumashyan, H.—Guričan, J.: Endomorphism kernel property for finite groups, Math. Bohem., https://mb.math.cas.cz/full/online1st/MB.2021.0171-20.pdf.