Correction to "Unique Factorization Domains"

1973 ◽  
Vol 80 (10) ◽  
pp. 1115
Author(s):  
P. M. Cohn
Keyword(s):  
Unique Factorization ◽  
Unique Factorization Domains

Additive decompositions of polynomials over unique factorization domains

2019 ◽  
Vol 19 (08) ◽  
pp. 2050150
Author(s):  
Leila Benferhat ◽  
Safia Manar Elislam Benoumhani ◽  
Rachid Boumahdi ◽  
Jesse Larone
Keyword(s):  
Finite Fields ◽  
Unique Factorization ◽  
Additive Decomposition ◽  
Unique Factorization Domains

Additive decompositions over finite fields were extensively studied by Brawely and Carlitz. In this paper, we study the additive decomposition of polynomials over unique factorization domains.

scholarly journals Euclid Prime Sequences over Unique Factorization Domains

2008 ◽  
Vol 17 (2) ◽  
pp. 145-152 ◽  
Author(s):  
Nobushige Kurokawa ◽  
Takakazu Satoh
Keyword(s):  
Unique Factorization ◽  
Unique Factorization Domains

scholarly journals On unique factorization domains

2011 ◽  
Vol 332 (1) ◽  
pp. 62-70 ◽  
Author(s):  
Jim Coykendall ◽  
William W. Smith
Keyword(s):  
Unique Factorization ◽  
Unique Factorization Domains

Atomic rings and the ascending chain condition for principal ideals

1974 ◽  
Vol 75 (3) ◽  
pp. 321-329 ◽  
Author(s):  
Anne Grams
Keyword(s):  
Polynomial Ring ◽  
Chain Condition ◽  
Noetherian Rings ◽  
Unique Factorization ◽  
Maximum Condition ◽  
Maximum Element ◽  
Principal Ideals ◽  
Set Containment ◽  
Unique Factorization Domains ◽  
Ascending Chain Condition

LetRbe a commutative ring. We say thatRsatisfies theascending chain condition for principal ideals, or thatRhasproperty(M), if each ascending sequence (a1) ⊆ (a2) ⊆ … of principal ideals ofRterminates. Property (M) is equivalent to themaximum condition on principal ideals; that is, under the partial order of set containment, each collection of principal ideals ofRhas a maximum element. Noetherian rings, of course, have property (M), but the converse is not true; for ifRhas property (M) and if {Xλ} is a set of indeterminates overR, then the polynomial ringR[{Xλ}] has property (M). Krull domains, and hence unique factorization domains, have property (M).

Almost excellent unique factorization domains

2020 ◽  
Vol 13 (1) ◽  
pp. 165-180
Author(s):  
Sarah M. Fleming ◽  
Susan Loepp
Keyword(s):  
Unique Factorization ◽  
Unique Factorization Domains
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