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Weakly integrally closed domains and forbidden patterns
 Date Issued:
 2009
 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.
Title:  Weakly integrally closed domains and forbidden patterns. 
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Name(s): 
Hopkins, Mary E. Charles E. Schmidt College of Science Department of Mathematical Sciences 

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. 

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

Persistent Link to This Record:  http://purl.flvc.org/FAU/199327  
Use and Reproduction:  http://rightsstatements.org/vocab/InC/1.0/  
Host Institution:  FAU 