AbstractIn this paper we generalize the standard notion of unique factorization domains to the nonatomic situation. The main result of this paper is that, in contrast to the atomic situation, the assumption that every irreducible is prime (atoms prime) and the notion that every (atomic) nonzero nonunit can be factored uniquely into irreducible elements are distinct notions
AbstractWe study examples of atomic domains which fail to satisfy the a.c.c. on principal ideals
AbstractLet D be a unique factorization domain and S an infinite subset of D. If f(X) is an element ...
In this thesis we study ideals in Dedekind domains, which factorize uniquely into a product of prime...
AbstractIn this paper we generalize the standard notion of unique factorization domains to the nonat...
Abstract. In this paper we generalize the standard notion of “unique fac-torization domains ” (UFDs)...
AbstractLet R be an integral domain. In this paper, we introduce a sequence of factorization propert...
Abstract In this paper we attempt to generalize the notion of “unique factorization domain” in the s...
AbstractWe show in this paper that given any reduced, cancellative, torsion-free, atomic monoid, it ...
AbstractIn this paper we attempt to generalize the notion of “unique factorization domain” in the sp...
AbstractAmong other results, we obtain here a normal atomic domain A such that A[X] is not atomic bu...
AbstractLet A be a commutative domain. We prove that both implications Aatomic⇒A[[X]]atomic, and A[[...
AbstractIn this paper, we study several factorization properties in an integral domain which are wea...
A ring has bounded factorizations if every cancellative nonunit a ...
The fundamental theorem of arithmetic says that any integer greater than 2 can be written uniquely a...
The commutative theory of Unique Factorisation Domains (UFDs) is well-developed (see, for example, Z...
AbstractWe study examples of atomic domains which fail to satisfy the a.c.c. on principal ideals
AbstractLet D be a unique factorization domain and S an infinite subset of D. If f(X) is an element ...
In this thesis we study ideals in Dedekind domains, which factorize uniquely into a product of prime...
AbstractIn this paper we generalize the standard notion of unique factorization domains to the nonat...
Abstract. In this paper we generalize the standard notion of “unique fac-torization domains ” (UFDs)...
AbstractLet R be an integral domain. In this paper, we introduce a sequence of factorization propert...
Abstract In this paper we attempt to generalize the notion of “unique factorization domain” in the s...
AbstractWe show in this paper that given any reduced, cancellative, torsion-free, atomic monoid, it ...
AbstractIn this paper we attempt to generalize the notion of “unique factorization domain” in the sp...
AbstractAmong other results, we obtain here a normal atomic domain A such that A[X] is not atomic bu...
AbstractLet A be a commutative domain. We prove that both implications Aatomic⇒A[[X]]atomic, and A[[...
AbstractIn this paper, we study several factorization properties in an integral domain which are wea...
A ring has bounded factorizations if every cancellative nonunit a ...
The fundamental theorem of arithmetic says that any integer greater than 2 can be written uniquely a...
The commutative theory of Unique Factorisation Domains (UFDs) is well-developed (see, for example, Z...
AbstractWe study examples of atomic domains which fail to satisfy the a.c.c. on principal ideals
AbstractLet D be a unique factorization domain and S an infinite subset of D. If f(X) is an element ...
In this thesis we study ideals in Dedekind domains, which factorize uniquely into a product of prime...
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