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In: Mathematica Slovaca, vol. 69, no. 2
George Georgescu - Claudia Mureşan

Going Up and Lying Over in congruence-modular algebras

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Year, pages: 2019, 275 - 296
Keywords: congruence-modular variety, commutator, prime congruence, Going Up, Lying Over

About article:

In this paper, we extend properties Going Up and Lying Over from ring theory to the general setting of congruence-modular equational classes, using the notion of prime congruence defined through the commutator. We show how these two properties relate to each other, prove that they are preserved by finite direct products and quotients and provide algebraic and topological characterizations for them. We also point out many kinds of varieties in which these properties always hold, generalizing the results of Belluce on MV-algebras and Rasouli and Davvaz on BL-algebras.

How to cite:

ISO 690:
Georgescu, G., Mureşan, C. 2019. Going Up and Lying Over in congruence-modular algebras. In Mathematica Slovaca, vol. 69, no.2, pp. 275-296. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0222

APA:
Georgescu, G., Mureşan, C. (2019). Going Up and Lying Over in congruence-modular algebras. Mathematica Slovaca, 69(2), 275-296. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0222

About edition:

Published: 27. 3. 2019