MULTIPLICATIVE SUBSETS OF ATOMS

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International Electronic Journal of Algebra
Volume:18 Issue:18
MULTIPLICATIVE SUBSETS OF ATOMS

MULTIPLICATIVE SUBSETS OF ATOMS

Pages : 107-116

View : 54 | Download : 12

Publication Date : 2015-12-01

Article Type : Research Paper

Abstract :A reduced, cancellative, torsion-free, commutative monoid M can be embedded in an integral domain R, where the atoms insert ignore into journalissuearticles values(irreducible elements); of M correspond to a subset of the atoms of R. This fact was used by J. Coykendall and B. Mammenga to show that for any reduced, cancellative, torsion-free, commutative, atomic monoid M, there exists an integral domain R with atomic factorization structure isomorphic to M. More generally, we show that any “nice” subset of atoms of R can be realized as the set of atoms of an integral domain T that contains R. We will also give several applications of this result.
Keywords : Cancellative commutative monoid, reduced monoid, atomic monoid, integral domain

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