# Finite basis problem for 2-testable monoids

Open Mathematics (2011)

- Volume: 9, Issue: 1, page 1-22
- ISSN: 2391-5455

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topEdmond Lee. "Finite basis problem for 2-testable monoids." Open Mathematics 9.1 (2011): 1-22. <http://eudml.org/doc/269230>.

@article{EdmondLee2011,

abstract = {A monoid S 1 obtained by adjoining a unit element to a 2-testable semigroup S is said to be 2-testable. It is shown that a 2-testable monoid S 1 is either inherently non-finitely based or hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five. Consequently, it is decidable in quadratic time if a finite 2-testable monoid is finitely based.},

author = {Edmond Lee},

journal = {Open Mathematics},

keywords = {Semigroups; Monoids; Varieties; Finitely based; Hereditarily finitely based; varieties of monoids; varieties of semigroups; finite basis problem; hereditarily finitely based monoids; inherently non-finitely based semigroups},

language = {eng},

number = {1},

pages = {1-22},

title = {Finite basis problem for 2-testable monoids},

url = {http://eudml.org/doc/269230},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Edmond Lee

TI - Finite basis problem for 2-testable monoids

JO - Open Mathematics

PY - 2011

VL - 9

IS - 1

SP - 1

EP - 22

AB - A monoid S 1 obtained by adjoining a unit element to a 2-testable semigroup S is said to be 2-testable. It is shown that a 2-testable monoid S 1 is either inherently non-finitely based or hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five. Consequently, it is decidable in quadratic time if a finite 2-testable monoid is finitely based.

LA - eng

KW - Semigroups; Monoids; Varieties; Finitely based; Hereditarily finitely based; varieties of monoids; varieties of semigroups; finite basis problem; hereditarily finitely based monoids; inherently non-finitely based semigroups

UR - http://eudml.org/doc/269230

ER -

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