On two classes of hereditarily finitely based semigroup identities

1982 ◽  
Vol 25 (1) ◽  
pp. 9-33 ◽  
Author(s):  
György Pollák
Keyword(s):  
Finitely Based ◽  
Hereditarily Finitely Based ◽  
Semigroup Identities

Hereditarily Finitely Based Semigroups of Triangular Matrices over Finite Fields

2013 ◽  
Vol 86 (2) ◽  
pp. 229-261 ◽  
Author(s):  
Wen Ting Zhang ◽  
Jian Rong Li ◽  
Yan Feng Luo
Keyword(s):  
Finite Fields ◽  
Finitely Based ◽  
Triangular Matrices ◽  
Hereditarily Finitely Based

On a question of Pollák and Volkov regarding hereditarily finitely based identities

2014 ◽  
Vol 68 (2) ◽  
pp. 128-134
Author(s):  
Edmond W. H. Lee
Keyword(s):  
Finitely Based ◽  
Hereditarily Finitely Based

On a hereditarily finitely based ai-semiring variety

2019 ◽  
Vol 23 (16) ◽  
pp. 6819-6825 ◽  
Author(s):  
Miaomiao Ren ◽  
Lingli Zeng
Keyword(s):  
Finitely Based ◽  
Hereditarily Finitely Based

Hereditarily finitely based monoids of extensive transformations

2009 ◽  
Vol 61 (1) ◽  
pp. 31-58 ◽  
Author(s):  
Edmond W. H. Lee
Keyword(s):  
Finitely Based ◽  
Hereditarily Finitely Based

scholarly journals The semiring variety generated by any finite number of finite fields and distributive lattices

2015 ◽  
Vol 98 (112) ◽  
pp. 45-51
Author(s):  
Yong Shao ◽  
Miaomiao Ren ◽  
Sinisa Crvenkovic ◽  
Melanija Mitrovic
Keyword(s):  
Finite Number ◽  
Distributive Lattice ◽  
Finite Fields ◽  
Distributive Lattices ◽  
Subdirectly Irreducible ◽  
Finitely Based ◽  
Hereditarily Finitely Based

In this paper we study the semiring variety V generated by any finite number of finite fields F1,..., Fk and two-element distributive lattice B2, i.e., V = HSP{B2, F1,..., Fk}. It is proved that V is hereditarily finitely based, and that, up to isomorphism, the two-element distributive lattice B2 and all subfields of F1,..., Fk are the only subdirectly irreducible semirings in V.

FINITELY BASED WORDS

2000 ◽  
Vol 10 (04) ◽  
pp. 457-480 ◽  
Author(s):  
OLGA SAPIR
Keyword(s):  
Sufficient Conditions ◽  
Basis Property ◽  
Free Monoid ◽  
Finite Basis ◽  
Finitely Based ◽  
Finite Basis Property ◽  
Letter Alphabet ◽  
Finite Language ◽  
Rees Quotient ◽  
The Ideal

Let W be a finite language and let Wc be the closure of W under taking subwords. Let S(W) denote the Rees quotient of a free monoid over the ideal consisting of all words that are not in Wc. We call W finitely based if the monoid S(W) is finitely based. Although these semigroups have easy structure they behave "generically" with respect to the finite basis property [6]. In this paper, we describe all finitely based words in a two-letter alphabet. We also find some necessary and some sufficient conditions for a set of words to be finitely based.

A JUST NON-FINITELY BASED VARIETY OF BIGROUPS

2001 ◽  
Vol 29 (9) ◽  
pp. 4011-4046 ◽  
Author(s):  
C. K. Gupta* ◽  
A. N. Krasilnikov
Keyword(s):  
Finitely Based ◽  
Finitely Based Variety

Varieties satisfying semigroup identities: Algebras over a finite field and rings

2016 ◽  
Vol 26 (05) ◽  
pp. 985-1017
Author(s):  
Olga B. Finogenova
Keyword(s):  
Finite Field ◽  
Associative Algebras ◽  
Adjoint Semigroup ◽  
Semigroup Identities ◽  
Associative Rings

We study varieties of associative algebras over a finite field and varieties of associative rings satisfying semigroup or adjoint semigroup identities. We characterize these varieties in terms of “forbidden algebras” and discuss some corollaries of the characterizations.

scholarly journals POSITIVE FRAGMENTS OF RELEVANCE LOGIC AND ALGEBRAS OF BINARY RELATIONS

2010 ◽  
Vol 4 (1) ◽  
pp. 81-105 ◽  
Author(s):  
ROBIN HIRSCH ◽  
SZABOLCS MIKULÁS
Keyword(s):  
Equational Theory ◽  
Relevance Logic ◽  
Binary Relations ◽  
Finitely Based ◽  
Similarity Type ◽  
Relation Composition

We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.

A general finite basis condition for systems of semigroup identities

1990 ◽  
Vol 41 (1) ◽  
pp. 181-191 ◽  
Author(s):  
M. V. Volkov
Keyword(s):  
Finite Basis ◽  
Semigroup Identities
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