Unique Factorization

1982 ◽  
pp. 1-16
Author(s):  
Kenneth Ireland ◽  
Michael Rosen
Keyword(s):  
Unique Factorization

scholarly journals The Complexity of Primes in Computable Unique Factorization Domains

2018 ◽  
Vol 59 (2) ◽  
pp. 139-156
Author(s):  
Damir D. Dzhafarov ◽  
Joseph R. Mileti
Keyword(s):  
Unique Factorization ◽  
Unique Factorization Domains

Unique factorization results for semigroups of L-functions

2008 ◽  
Vol 341 (3) ◽  
pp. 517-527 ◽  
Author(s):  
Jerzy Kaczorowski ◽  
Giuseppe Molteni ◽  
Alberto Perelli
Keyword(s):  
Unique Factorization

CANCELLATION LAW AND UNIQUE FACTORIZATION THEOREM FOR STRING OPERATIONS

2006 ◽  
Vol 05 (02) ◽  
pp. 231-243
Author(s):  
DONGVU TONIEN
Keyword(s):  
Abelian Group ◽  
Algebraic Structure ◽  
Additive Group ◽  
New Product ◽  
Binary String ◽  
Factorization Theorem ◽  
General Criterion ◽  
Unique Factorization ◽  
Product Operation ◽  
Associative Law

Recently, Hoit introduced arithmetic on blocks, which extends the binary string operation by Jacobs and Keane. A string of elements from the Abelian additive group of residues modulo m, (Zm, ⊕), is called an m-block. The set of m-blocks together with Hoit's new product operation form an interesting algebraic structure where associative law and cancellation law hold. A weaker form of unique factorization and criteria for two indecomposable blocks to commute are also proved. In this paper, we extend Hoit's results by replacing the Abelian group (Zm, ⊕) by an arbitrary monoid (A, ◦). The set of strings built up from the alphabet A is denoted by String(A). We extend the operation ◦ on the alphabet set A to the string set String(A). We show that (String(A), ◦) is a monoid if and only if (A, ◦) is a monoid. When (A, ◦) is a group, we prove that stronger versions of a cancellation law and unique factorization hold for (String(A), ◦). A general criterion for two irreducible strings to commute is also presented.

scholarly journals Unique factorization of matrices and Towber rings

1979 ◽  
Vol 59 (2) ◽  
pp. 387-394 ◽  
Author(s):  
Dennis R Estes ◽  
Jacob R Matijevic
Keyword(s):  
Unique Factorization
Sign in / Sign up

Export Citation Format

Share Document