In Prüfer domains of finite character, ideals are represented as finite intersections of special ideals which are proper generalizations of the classical primary ideals. We show that representations of ideals as shortest intersections of primal or quasi-primary ideals exist and are unique. Moreover, every non-zero ideal is the product of uniquely determined pairwise comaximal quasi-primary ideals. Semigroups of primal and quasi-primary ideals with fixed associated primes are also investigated in arbitrary Prüfer domains. Their structures can be described in terms of the value groups of localizations
Given a star operation * of finite type, we call a domain R a *-unique representation domain (*-URD)...
summary:We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative ring...
summary:We explore the connection between atomicity in Prüfer domains and their corresponding class ...
In Prüfer domains of finite character, ideals are represented as finite intersections of special ide...
AbstractIn Prüfer domains of finite character, ideals are represented as finite intersections of spe...
In studying unique factorization of domains we encountered a property of ideals. Using that we defin...
AbstractWe relate ideals in commutative rings which are products of primary ideals to ideals with pr...
The primary purpose of this paper is give a classification scheme for the nonzero primes of a Pr\"uf...
AbstractThe ring-theoretical concept of semiprime ideal is appropriately defined for lattices. We pr...
An ideal I of a commutative ring D with identity is called an SFT ideal if there exist a finitely ge...
AbstractGiven a star operation ∗ of finite type, we call a domain R a ∗-unique representation domain...
AbstractWe describe classes of prime ideals in ultraproducts of commutative rings. We consider in pa...
Abstract. Weakly prime ideals in a commutative ring with non-zero identity have been introduced and ...
AbstractIn this paper we investigate regularly generated, regular, semiregular, and faithful ideals ...
In this thesis we study ideals in Dedekind domains, which factorize uniquely into a product of prime...
Given a star operation * of finite type, we call a domain R a *-unique representation domain (*-URD)...
summary:We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative ring...
summary:We explore the connection between atomicity in Prüfer domains and their corresponding class ...
In Prüfer domains of finite character, ideals are represented as finite intersections of special ide...
AbstractIn Prüfer domains of finite character, ideals are represented as finite intersections of spe...
In studying unique factorization of domains we encountered a property of ideals. Using that we defin...
AbstractWe relate ideals in commutative rings which are products of primary ideals to ideals with pr...
The primary purpose of this paper is give a classification scheme for the nonzero primes of a Pr\"uf...
AbstractThe ring-theoretical concept of semiprime ideal is appropriately defined for lattices. We pr...
An ideal I of a commutative ring D with identity is called an SFT ideal if there exist a finitely ge...
AbstractGiven a star operation ∗ of finite type, we call a domain R a ∗-unique representation domain...
AbstractWe describe classes of prime ideals in ultraproducts of commutative rings. We consider in pa...
Abstract. Weakly prime ideals in a commutative ring with non-zero identity have been introduced and ...
AbstractIn this paper we investigate regularly generated, regular, semiregular, and faithful ideals ...
In this thesis we study ideals in Dedekind domains, which factorize uniquely into a product of prime...
Given a star operation * of finite type, we call a domain R a *-unique representation domain (*-URD)...
summary:We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative ring...
summary:We explore the connection between atomicity in Prüfer domains and their corresponding class ...