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Weakly integrally closed domains and forbidden patterns
| Title: | Weakly integrally closed domains and forbidden patterns. |
 122 views 41 downloads |
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| Name(s): |
Hopkins, Mary E. Charles E. Schmidt College of Science Department of Mathematical Sciences |
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| Type of Resource: | text | |
| Genre: | Electronic Thesis Or Dissertation | |
| Date Issued: | 2009 | |
| Publisher: | Florida Atlantic University | |
| Physical Form: | electronic | |
| Extent: | v, 39 p. | |
| Language(s): | English | |
| Summary: | 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 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. | |
| Identifier: | 351399009 (oclc), 199327 (digitool), FADT199327 (IID), fau:3003 (fedora) | |
| Note(s): |
by Mary E. Hopkins. Thesis (Ph.D.)--Florida Atlantic University, 2009. Includes bibliography. Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web. |
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| Subject(s): |
Mathematical analysis Algebra, Homological Monoids Categories (Mathematics) Semigroup algebras |
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| Persistent Link to This Record: | http://purl.flvc.org/FAU/199327 | |
| Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
| Host Institution: | FAU |
