On a result of James and Niven concerning unique factorization in congruence semigroups | Zendy

M. Banister | Zendy; Jon Chaika | Zendy; Scott T. Chapman | Zendy; William Meyerson | Zendy

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On a result of James and Niven concerning unique factorization in congruence semigroups

Author(s) -

M. Banister,

Jon Chaika,

Scott T. Chapman,

William Meyerson

Publication year - 2007

Publication title -

elemente der mathematik

Language(s) - English

Resource type - Journals

eISSN - 1420-8962

pISSN - 0013-6018

DOI - 10.4171/em/56

Subject(s) - multiplicative function , mathematics , semigroup , congruence (geometry) , uniqueness , factorization , unique factorization domain , pure mathematics , natural number , discrete mathematics , algebra over a field , mathematical analysis , algorithm , geometry

The theory of non-unique factorizations in integral domains and monoids is a very active area of current research (see both [1] and [4] to view re-cent trends in this work). To demonstrate the phenomena of non-unique factorizations, we consider a result from the classical setting on uniqueness of factorizations by James and Niven [11]. We proceed as follows. Let N represent the natural numbers and suppose that M N is a multiplicative semigroup. M is called a congruence semigroup if there exists a natural number n such that

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