nLab
Bézout monoid
Contents
Context
Algebra
Monoid theory
monoid theory in algebra:
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monoid, infinity-monoid
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monoid object, monoid object in an (infinity,1)-category
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Mon, CMon
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monoid homomorphism
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trivial monoid
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submonoid, quotient monoid?
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divisor, multiple?, quotient element?
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inverse element, unit, irreducible element
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ideal in a monoid
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principal ideal in a monoid
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commutative monoid
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cancellative monoid
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GCD monoid
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unique factorization monoid
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Bézout monoid
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principal ideal monoid
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group, abelian group
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absorption monoid
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free monoid, free commutative monoid
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graphic monoid
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monoid action
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module over a monoid
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localization of a monoid
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group completion
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endomorphism monoid
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super commutative monoid
Contents
Definition
A monoid (or semigroup) is a left Bézout monoid if all finitely generated left ideals of are left principal ideals in . Similarily, is a right Bézout monoid if all finitely generated right ideals of are right principal ideals. Finally, is a Bézout monoid if it is both a left Bézout monoid and a right Bézout monoid.
Last revised on May 21, 2021 at 22:26:26.
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