summary:We explore the connection between atomicity in Prüfer domains and their corresponding class groups. We observe that a class group of infinite order is necessary for non-Noetherian almost Dedekind and Prüfer domains of finite character to be atomic. We construct a non-Noetherian almost Dedekind domain and exhibit a generating set for the ideal class semigroup
summary:A nonzero $R$-module $M$ is atomic if for each two nonzero elements $a, b$ in $M$, both cycl...
AbstractWe study examples of atomic domains which fail to satisfy the a.c.c. on principal ideals
AbstractIn this paper we give an ideal-theoretical characterization of a distinguished class of Prüf...
summary:We explore the connection between atomicity in Prüfer domains and their corresponding class ...
The objective of this dissertation was to determine the class of domains that are both almost Dedeki...
Abstract. Let H be an atomic monoid. For k 2N let VkðHÞ denote the set of all m2N with the following...
In Prüfer domains of finite character, ideals are represented as finite intersections of special ide...
When we form a finite algebraic extension of Q, we are not guaranteed that the ring of integers, O, ...
AbstractIn Prüfer domains of finite character, ideals are represented as finite intersections of spe...
AbstractLet R be an integral domain with quotient field K and L⊃K a finite extension field. By an R-...
Abstract. A classical result of Claborn states that every abelian group is the class group of a comm...
AbstractAmong other results, we obtain here a normal atomic domain A such that A[X] is not atomic bu...
Dedekind domain are the rings in which every nonzero proper ideal has a prime factorization. In this...
In Section 0 we review the definition of the ideal completion of a join-semilattice, reviewing also ...
For a Dedekind domain D, let P.D/ be the set of ideals of D that are the radical of a principal idea...
summary:A nonzero $R$-module $M$ is atomic if for each two nonzero elements $a, b$ in $M$, both cycl...
AbstractWe study examples of atomic domains which fail to satisfy the a.c.c. on principal ideals
AbstractIn this paper we give an ideal-theoretical characterization of a distinguished class of Prüf...
summary:We explore the connection between atomicity in Prüfer domains and their corresponding class ...
The objective of this dissertation was to determine the class of domains that are both almost Dedeki...
Abstract. Let H be an atomic monoid. For k 2N let VkðHÞ denote the set of all m2N with the following...
In Prüfer domains of finite character, ideals are represented as finite intersections of special ide...
When we form a finite algebraic extension of Q, we are not guaranteed that the ring of integers, O, ...
AbstractIn Prüfer domains of finite character, ideals are represented as finite intersections of spe...
AbstractLet R be an integral domain with quotient field K and L⊃K a finite extension field. By an R-...
Abstract. A classical result of Claborn states that every abelian group is the class group of a comm...
AbstractAmong other results, we obtain here a normal atomic domain A such that A[X] is not atomic bu...
Dedekind domain are the rings in which every nonzero proper ideal has a prime factorization. In this...
In Section 0 we review the definition of the ideal completion of a join-semilattice, reviewing also ...
For a Dedekind domain D, let P.D/ be the set of ideals of D that are the radical of a principal idea...
summary:A nonzero $R$-module $M$ is atomic if for each two nonzero elements $a, b$ in $M$, both cycl...
AbstractWe study examples of atomic domains which fail to satisfy the a.c.c. on principal ideals
AbstractIn this paper we give an ideal-theoretical characterization of a distinguished class of Prüf...
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