Current Search: Algebra, Homological (x)
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Title
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Weakly integrally closed domains and forbidden patterns.
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Creator
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Hopkins, Mary E., Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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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
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2009
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PURL
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http://purl.flvc.org/FAU/199327
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Subject Headings
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Mathematical analysis, Algebra, Homological, Monoids, Categories (Mathematics), Semigroup algebras
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Format
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Document (PDF)
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Title
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Finite valuated groups.
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Creator
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Holroyd, Keiko Ito, Florida Atlantic University, Richman, Fred
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Abstract/Description
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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 p-groups 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 p-group to the simultaneous decomposition of a finite abelian p-group and a subgroup.
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Date Issued
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1996
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PURL
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http://purl.flvc.org/fcla/dt/15320
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Subject Headings
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Finite groups, Abelian groups, Abelian p-groups, Algebra, Homological
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Format
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Document (PDF)