Minimal formations of universal algebras

Wenbin Guo; K.P. Shum

Displaying similar documents to “Minimal formations of universal algebras”

On the lattice of congruences on inverse semirings

Anwesha Bhuniya, Anjan Kumar Bhuniya (2008)

Discussiones Mathematicae - General Algebra and Applications

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Let S be a semiring whose additive reduct (S,+) is an inverse semigroup. The relations θ and k, induced by tr and ker (resp.), are congruences on the lattice C(S) of all congruences on S. For ρ ∈ C(S), we have introduced four congruences $ρ_{m i n}, ρ_{m a x}, ρ^{m i n}$ and $ρ^{m a x}$ on S and showed that $ρ θ = [ρ_{m i n}, ρ_{m a x}]$ and $ρ κ = [ρ^{m i n}, ρ^{m a x}]$ . Different properties of ρθ and ρκ have been considered here. A congruence ρ on S is a Clifford congruence if and only if $ρ_{m a x}$ is a distributive lattice congruence and $ρ^{m a x}$ is a skew-ring congruence on S. If η (σ) is the...

The spt-crank for overpartitions

Frank G. Garvan, Chris Jennings-Shaffer (2014)

Acta Arithmetica

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Bringmann, Lovejoy, and Osburn (2009, 2010) showed that the generating functions of the spt-overpartition functions $\bar{s p t} (n)$ , ${\bar{s p t}}_{1} (n)$ , ${\bar{s p t}}_{2} (n)$ , and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews, Garvan, and Liang (2012) defined an spt-crank in terms of weighted vector partitions which combinatorially explain simple congruences modulo 5 and 7 for spt(n). Chen, Ji, and Zang (2013) were able to define this spt-crank in terms of ordinary partitions....

Factorable congruences and strict refinement.

Iskander, A.A. (1996)

Acta Mathematica Universitatis Comenianae. New Series

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Congruences for certain families of Apéry-like sequences

Zhi-Hong Sun (2022)

Czechoslovak Mathematical Journal

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We systematically investigate the expressions and congruences for both a one-parameter family ${G_{n} (x)}$ as well as a two-parameter family ${G_{n} (r, m)}$ of sequences.

Relation products of congruences and factor congruences

Jaromír Duda (1991)

Czechoslovak Mathematical Journal

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Integers not of the form $c (2^{a} + 2^{b}) + p^{α}$

Pingzhi Yuan (2004)

Acta Arithmetica

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Monadic $n \times m$ -valued Łukasiewicz-Moisil algebras

A. V. Figallo, Claudia A. Sanza (2012)

Mathematica Bohemica

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Here we initiate an investigation into the class $m L M_{n \times m}$ of monadic $n \times m$ -valued Łukasiewicz-Moisil algebras (or $m L M_{n \times m}$ -algebras), namely $n \times m$ -valued Łukasiewicz-Moisil algebras endowed with a unary operation. These algebras constitute a generalization of monadic $n$ -valued Łukasiewicz-Moisil algebras. In this article, the congruences on these algebras are determined and subdirectly irreducible algebras are characterized. From this last result it is proved that $m L M_{n \times m}$ is a discriminator variety and as a consequence,...

A scheme for congruence semidistributivity

Ivan Chajda, Eszter K. Horváth (2003)

Discussiones Mathematicae - General Algebra and Applications

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A diagrammatic statement is developed for the generalized semidistributive law in case of single algebras assuming that their congruences are permutable. Without permutable congruences, a diagrammatic statement is developed for the ∧-semidistributive law.