Current Search: Algebra, Homological (x)


Title

Weakly integrally closed domains and forbidden patterns.

Creator

Hopkins, Mary E., Charles E. Schmidt College of Science, Department of Mathematical Sciences

Abstract/Description

An integral domain D is weakly integrally closed if whenever there is an element x in the quotient field of D and a nonzero finitely generated ideal J of D such that xJ J2, then x is in D. We define weakly integrally closed numerical monoids similarly. If a monoid algebra is weakly integrally closed, then so is the monoid. A pattern F of finitely many 0's and 1's is forbidden if whenever the characteristic binary string of a numerical monoid M contains F, then M is not weakly integrally...
Show moreAn integral domain D is weakly integrally closed if whenever there is an element x in the quotient field of D and a nonzero finitely generated ideal J of D such that xJ J2, then x is in D. We define weakly integrally closed numerical monoids similarly. If a monoid algebra is weakly integrally closed, then so is the monoid. A pattern F of finitely many 0's and 1's is forbidden if whenever the characteristic binary string of a numerical monoid M contains F, then M is not weakly integrally closed. Any stretch of the pattern 11011 is forbidden. A numerical monoid M is weakly integrally closed if and only if it has a forbidden pattern. For every finite set S of forbidden patterns, there exists a monoid that is not weakly integrally closed and that contains no stretch of a pattern in S. It is shown that particular monoid algebras are weakly integrally closed.
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Date Issued

2009

PURL

http://purl.flvc.org/FAU/199327

Subject Headings

Mathematical analysis, Algebra, Homological, Monoids, Categories (Mathematics), Semigroup algebras

Format

Document (PDF)


Title

Finite valuated groups.

Creator

Holroyd, Keiko Ito, Florida Atlantic University, Richman, Fred

Abstract/Description

The concept of valuated groups, simply presented groups, and simultaneous decomposition of an abelian group and a subgroup are discussed. We classify the structure of finite valuated pgroups of order up p^4. With a refinement of a classical theorem on bounded pure subgroups, we also relate the decomposition of a finite valuated pgroup to the simultaneous decomposition of a finite abelian pgroup and a subgroup.

Date Issued

1996

PURL

http://purl.flvc.org/fcla/dt/15320

Subject Headings

Finite groups, Abelian groups, Abelian pgroups, Algebra, Homological

Format

Document (PDF)