Algebra universalis, ISSN 0002-5240, 11/2015, Volume 74, Issue 3, pp. 333 - 350

We prove a sufficient condition under which a semigroup admits no finite identity basis. As an application, it is shown that the identities of the Kauffman...

involution semigroup | Primary: 20M07 | Algebra | finite basis problem | variety | Kauffman monoid | Rees matrix semigroup | semigroup | Mathematics | semigroup identity | wire monoid | MATHEMATICS | SEMIGROUPS | EQUATIONAL THEORIES | VARIETIES | Computer science

involution semigroup | Primary: 20M07 | Algebra | finite basis problem | variety | Kauffman monoid | Rees matrix semigroup | semigroup | Mathematics | semigroup identity | wire monoid | MATHEMATICS | SEMIGROUPS | EQUATIONAL THEORIES | VARIETIES | Computer science

Journal Article

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, ISSN 0004-9727, 02/2020, Volume 101, Issue 1, pp. 88 - 104

Let Tn(F) be the semigroup of all upper triangular n n matrices over a field F. Let UTn(F) and UT 1 n (F) be subsemigroups of Tn(F), respectively, having 0s...

MATHEMATICS | BASES | finite basis problem | EQUATIONAL THEORIES | IDENTITIES | variety | semigroup | matrix | identity basis

MATHEMATICS | BASES | finite basis problem | EQUATIONAL THEORIES | IDENTITIES | variety | semigroup | matrix | identity basis

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2016, Volume 368, Issue 3, pp. 2115 - 2143

is finitely axiomatizable. This provides a common generalization of R. McKenzie's finite basis theorem for congruence modular varieties with a finite residual...

MATHEMATICS | CONGRUENCE LATTICES | ALGEBRAS | IDENTITIES | EQUATIONAL BASES | COMMUTATOR | DISTRIBUTIVITY

MATHEMATICS | CONGRUENCE LATTICES | ALGEBRAS | IDENTITIES | EQUATIONAL BASES | COMMUTATOR | DISTRIBUTIVITY

Journal Article

Demonstratio Mathematica, ISSN 0420-1213, 12/2015, Volume 48, Issue 4, pp. 475 - 492

In an earlier paper, the second-named author has described the identities holding in the so-called Catalan monoids. Here we extend this description to a...

Hecke-Kiselman monoids | equational theory | finite basis problem | semigroup identity | Kiselman monoids | Catalan monoids | Finite basis problem | Semigroup identity | Equational theory

Hecke-Kiselman monoids | equational theory | finite basis problem | semigroup identity | Kiselman monoids | Catalan monoids | Finite basis problem | Semigroup identity | Equational theory

Journal Article

LMS Journal of Computation and Mathematics, ISSN 1461-1570, 04/2015, Volume 18, Issue 1, pp. 1 - 129

Two semigroups are distinct if they are neither isomorphic nor anti-isomorphic. Although there exist 15 973 pairwise distinct semigroups of order six, only...

MATHEMATICS | MATHEMATICS, APPLIED | IDENTITY BASES | EQUATIONAL BASES | VARIETIES | MONOIDS | BASIS QUESTION

MATHEMATICS | MATHEMATICS, APPLIED | IDENTITY BASES | EQUATIONAL BASES | VARIETIES | MONOIDS | BASIS QUESTION

Journal Article

Discrete Mathematics and Theoretical Computer Science, ISSN 1462-7264, 2016, Volume 17, Issue 3, pp. 179 - 202

Epigroups are semigroups equipped with an additional unary operation called pseudoinversion. Each finite semigroup can be considered as an epigroup. We prove...

Finite basis problem | Epigroup | Decidability of equational theory | Finite semigroup | Combinatorics | Theorems | Computer Science | Discrete Mathematics

Finite basis problem | Epigroup | Decidability of equational theory | Finite semigroup | Combinatorics | Theorems | Computer Science | Discrete Mathematics

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 02/2019, Volume 69, Issue 1, pp. 15 - 34

In this paper, we investigate the variety of regular double -algebras and its subvarieties , ≥ 1, of range . First, we present an explicit description of the...

08B15 | equational basis | 06D50 | Priestley duality | discriminator variety | algebra | simple algebra | subdirectly irreducible algebra | regular double | lattice of subvarieties | double Heyting algebra | Secondary 08B26 | Primary 06D15 | 03G25 | 03G10 | regular double p-algebra | MATHEMATICS | SPACES | HEYTING ALGEBRAS | EQUATIONAL CLASSES | Algebra

08B15 | equational basis | 06D50 | Priestley duality | discriminator variety | algebra | simple algebra | subdirectly irreducible algebra | regular double | lattice of subvarieties | double Heyting algebra | Secondary 08B26 | Primary 06D15 | 03G25 | 03G10 | regular double p-algebra | MATHEMATICS | SPACES | HEYTING ALGEBRAS | EQUATIONAL CLASSES | Algebra

Journal Article

Algebra and Logic, ISSN 0002-5232, 5/2016, Volume 55, Issue 2, pp. 146 - 172

Different types of compactness in the Zariski topology are explored: for instance, equational Noetherianity, equational Artinianity, qω-compactness, and...

metacompact algebras | equationally Artinian algebras | equationally Noetherian algebras | Mathematics | u ω -compactness | algebraic sets | q ω -compactness | equations | algebraic structures | coordinate algebra | Algebra | varieties | radical ideal | equational domains | free algebras | Zariski topology | metacompact spaces | prevarieties | Mathematical Logic and Foundations | Hilbert’s basis theorem | compactness | ELEMENTARY THEORY | q(omega)-compactness | LOGIC | Hilbert's basis theorem | MATHEMATICS | THEOREMS | u(omega)-compactness | Analysis | Geometry, Algebraic

metacompact algebras | equationally Artinian algebras | equationally Noetherian algebras | Mathematics | u ω -compactness | algebraic sets | q ω -compactness | equations | algebraic structures | coordinate algebra | Algebra | varieties | radical ideal | equational domains | free algebras | Zariski topology | metacompact spaces | prevarieties | Mathematical Logic and Foundations | Hilbert’s basis theorem | compactness | ELEMENTARY THEORY | q(omega)-compactness | LOGIC | Hilbert's basis theorem | MATHEMATICS | THEOREMS | u(omega)-compactness | Analysis | Geometry, Algebraic

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 2003, Volume 293, Issue 1, pp. 169 - 188

This paper shows that the collection of identities which hold in the algebra N of the natural numbers with constant zero, and binary operations of sum and...

Equational logic | Complete axiomatizations | Exponential time complexity | Varieties | BISIMULATION | ITERATION | varieties | exponential time complexity | complete axiomatizations | COMPUTER SCIENCE, THEORY & METHODS | equational logic

Equational logic | Complete axiomatizations | Exponential time complexity | Varieties | BISIMULATION | ITERATION | varieties | exponential time complexity | complete axiomatizations | COMPUTER SCIENCE, THEORY & METHODS | equational logic

Journal Article

International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems, ISSN 0218-4885, 12/2015, Volume 23, pp. 31 - 42

The main concern of this paper is with the equations satisfied by the algebra of truth values of type-2 fuzzy sets. That algebra has elements all mappings from...

equational basis | locally finite | variety | Type-2 fuzzy set | convolution | semilattice | truth value algebra | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

equational basis | locally finite | variety | Type-2 fuzzy set | convolution | semilattice | truth value algebra | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal Article

DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, ISSN 1462-7264, 2016, Volume 17, Issue 3, pp. 179 - 202

Epigroups are semigroups equipped with an additional unary operation called pseudoinversion. Each finite semigroup can be considered as an epigroup. We prove...

COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | finite basis problem | finite semigroup | decidability of equational theory | epigroup

COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | finite basis problem | finite semigroup | decidability of equational theory | epigroup

Journal Article

Algebra Universalis, ISSN 0002-5240, 01/2005, Volume 52, Issue 2-3, pp. 289 - 302

Ross Willard proved that every congruence meet-semidistributive variety of algebras that has a finite residual bound and a finite signature can be axiomatized...

Finitely based | Variety | Congruence meet-semi-distributive | Equational theory | MATHEMATICS | equational theory | ALGEBRAS | variety | EQUATIONAL BASES | finitely based | congruence meet-semidistributive

Finitely based | Variety | Congruence meet-semi-distributive | Equational theory | MATHEMATICS | equational theory | ALGEBRAS | variety | EQUATIONAL BASES | finitely based | congruence meet-semidistributive

Journal Article

algebra universalis, ISSN 0002-5240, 1/2005, Volume 52, Issue 2, pp. 289 - 302

Ross Willard proved that every congruence meet-semidistributive variety of algebras that has a finite residual bound and a finite signature can be axiomatized...

08B05 | Algebra | variety | 03C05 | Mathematics | finitely based | congruence meet-semidistributive | Equational theory

08B05 | Algebra | variety | 03C05 | Mathematics | finitely based | congruence meet-semidistributive | Equational theory

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 7/1997, Volume 349, Issue 7, pp. 2755 - 2774

R. McKenzie has recently associated to each Turing machine T a finite algebra A(T) having some remarkable properties. We add to the list of properties, by...

Universal algebra | Algebra | Turing machines | Lindenbaum Tarski algebra | Subalgebras | Quasiidentities | Mathematical logic | Mathematics | Mathematical congruence | Polls | Finitely axiomatizable | Equational theory | Finite algebra | MATHEMATICS | finitely axiomatizable | equational theory | finite algebra | CONGRUENCE | K PQ MATHEMATICS

Universal algebra | Algebra | Turing machines | Lindenbaum Tarski algebra | Subalgebras | Quasiidentities | Mathematical logic | Mathematics | Mathematical congruence | Polls | Finitely axiomatizable | Equational theory | Finite algebra | MATHEMATICS | finitely axiomatizable | equational theory | finite algebra | CONGRUENCE | K PQ MATHEMATICS

Journal Article

15.
Full Text
A Finite Basis Theorem for Residually Finite, Congruence Meet-Semidistributive Varieties

The Journal of Symbolic Logic, ISSN 0022-4812, 3/2000, Volume 65, Issue 1, pp. 187 - 200

We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is...

Universal algebra | Algebra | Mathematical theorems | Logical theorems | Cardinality | Lindenbaum Tarski algebra | Plant roots | Universalism | Mathematical congruence | Children | Residually finite | Congruence meet-semidistributive | Finitely based | Variety | Equational theory | MATHEMATICS | equational theory | finitely based | congruence meet-semidistributive | variety | residually finite | Congruences and residues | Analysis | Symbolic and mathematical logic | 08B05 | Finitely Based | 03C05 | Equational Theory | Residually Finite | Congruence Meet-Semidistributive

Universal algebra | Algebra | Mathematical theorems | Logical theorems | Cardinality | Lindenbaum Tarski algebra | Plant roots | Universalism | Mathematical congruence | Children | Residually finite | Congruence meet-semidistributive | Finitely based | Variety | Equational theory | MATHEMATICS | equational theory | finitely based | congruence meet-semidistributive | variety | residually finite | Congruences and residues | Analysis | Symbolic and mathematical logic | 08B05 | Finitely Based | 03C05 | Equational Theory | Residually Finite | Congruence Meet-Semidistributive

Journal Article

Journal of the ACM (JACM), ISSN 0004-5411, 07/1993, Volume 40, Issue 3, pp. 477 - 503

Journal Article

Semigroup Forum, ISSN 0037-1912, 10/2006, Volume 73, Issue 2, pp. 308 - 312

We sharpen the main results in [1] by finding short equational bases for two varieties of groupoids associated with involuted restrictive bisemigroups of...

Mathematics | Algebra | equational basis | MATHEMATICS | groupoid | bisemigroup

Mathematics | Algebra | equational basis | MATHEMATICS | groupoid | bisemigroup

Journal Article

Semigroup Forum, ISSN 0037-1912, 4/2011, Volume 82, Issue 2, pp. 296 - 306

The graph of an algebra A is the relational structure G(A) in which the relations are the graphs of the basic operations of A. Let denote by the class of all...

Mathematics | Finite axiomatizability | Algebra | Graphs of semigroups | Finite quasi-equational bases | Quasivarieties of relational structures | MATHEMATICS | FINITE BASIS | Universities and colleges

Mathematics | Finite axiomatizability | Algebra | Graphs of semigroups | Finite quasi-equational bases | Quasivarieties of relational structures | MATHEMATICS | FINITE BASIS | Universities and colleges

Journal Article

Algebra Universalis, ISSN 0002-5240, 2010, Volume 63, Issue 2-3, pp. 171 - 186

Let G be the group generated by delta of finite order n and let a and b be integers such that G is generated by delta(a) and delta(b). We write Sigma(n)(a,b)...

self-dual | uniform identity | interchange law | finitely based | medial groupoid | independent basis | MATHEMATICS | EQUATIONAL THEORIES

self-dual | uniform identity | interchange law | finitely based | medial groupoid | independent basis | MATHEMATICS | EQUATIONAL THEORIES

Journal Article

Information Processing Letters, ISSN 0020-0190, 2008, Volume 108, Issue 5, pp. 284 - 289

This paper studies the equational theory of prebisimilarity, a bisimulation-based preorder introduced by Hennessy and Milner in the early 1980s, over basic CCS...

Process algebra | Finite basis | Basic CCS | Divergence | Concurrency | Prebisimilarity | Complete axiomatisation | Non-finitely based equational theory | Equational theory | BISIMULATION | COMPUTER SCIENCE, INFORMATION SYSTEMS

Process algebra | Finite basis | Basic CCS | Divergence | Concurrency | Prebisimilarity | Complete axiomatisation | Non-finitely based equational theory | Equational theory | BISIMULATION | COMPUTER SCIENCE, INFORMATION SYSTEMS

Journal Article

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