monoid


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monoid

[′mä‚nȯid]
(mathematics)
A semigroup which has an identity element.

monoid

An operator * and a value x form a monoid if * is associative and x is its left and right identity.
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1) is a commutative monoid and the following conditions hold for all x, y, z [member of] A,
a] : a [member of] A} of M by open sets indexed by a set A, a schedule is an element of the monoid SA = [(A x [R.
m] is a monoid (semigroup with an identity) under composition of partial transformations, usually called the symmetric inverse semigroup on m letters.
Their analysis of these Markov chains took advantage of the monoid structure on the set of faces.
A t-norm is a continuous mapping * : [0,1] x [0,1] [right arrow] [0,1] such that ([0,1], *) is abelian monoid with unit one and c * d [greater than or equal to] a * b if c [greater than or equal to] a and d [greater than or equal to] b for all a, b, c [member of] [0,1].
Marimuthu (2003) An Object-Oriented Query Processor Based on an Extended Monoid Algebra, M.
China) treats the stable range condition as an element-wise condition on rings in its own right, but also shows its relationship to such topics as cancellation, of modules, comparability of modules, cleanness, K-theory, monoid theory, matrix theory, and topology.
left S-posets, (T, S)-biposets), where the morphisms are order and monoid action preserving mappings.
A monoid S satisfies Condition (K) if every left collapsible submonoid of S contains a left zero.
Examples include simultaneous surface resolution in quadratic and biquadratic Galois extensions, asymptotic behavior of cohomology, conic divisor classes over a normal monoid algebra, Rees algebras of the second syzygy module of the residue field of a regular local ring, a local global principle for the elementary unimodular vector group, picture invariants and the isomorphism problem for complex semisimple Lie algebras, arithmetic rank of certain Segre products, and strong semistability and Hilbert-Kunz multiplicity for singular plane curves.
When useful, M will be identified with the corresponding set of monomials belonging to the free monoid [T.