Meet infinite distributivity for congruence lattices of direct sums of algebras
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Heghine Ghumashyan
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.
The first author thanks the NSP of the Slovak republic, SAIA and the Comenius University Bratislava for the support. The second author was supported by VEGA grant No. 1/0333/17 of Slovak Republic.
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(Communicated by Miroslav Ploščica)
Acknowledgement
We thank the anonymous referee for the detailed review and suggestions which helped to improve our presentation.
References
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Articles in the same Issue
- Regular Papers
- Logical and algebraic properties of generalized orthomodular posets
- Integral prefilters and integral Eq-algebras
- Modules with fusion and implication based over distributive lattices: Representation and duality
- Localization of k × j-rough Heyting algebras
- Meet infinite distributivity for congruence lattices of direct sums of algebras
- Some exponential diophantine equations II: The equation x2 – Dy2 = kz for even k
- On extensions of the Open Door Lemma
- Nevanlinna theory for holomophic curves from annuli into semi-Abelian varieties
- Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions
- On the behaviour solutions of fractional and partial integro differential heat equations and its numerical solutions
- Oscillatory and asymptotic behavior of solutions of third-order quasi-linear neutral difference equations
- Some properties of Kantorovich variant of Chlodowsky-Szász operators induced by Boas-Buck type polynomials
- A Study on statistical versions of convergence of sequences of functions
- Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps
- Notes on affine Killing and two-Killing vector fields
- Prediction of the exponential fractional upper record-values
- On concomitants of generalized order statistics from generalized FGM family under a general setting
- One-parameter generalization of dual-hyperbolic Pell numbers
