The search session has expired. Please query the service again.
Let be a commutative ring with nonzero identity, let be the set of all ideals of and an expansion of ideals of defined by . We introduce the concept of -primary ideals in commutative rings. A proper ideal of is called a -primary ideal if whenever and , then or . Our purpose is to extend the concept of -ideals to -primary ideals of commutative rings. Then we investigate the basic properties of -primary ideals and also discuss the relations among -primary, -primary and...
It is proved that a Marot ring is a Krull ring if and only if its monoid of regular elements is a Krull monoid.
We study the multiplicative lattices which satisfy the condition for all . Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group or . A sharp lattice localized at its maximal elements are totally ordered sharp lattices. The converse is true if has finite character.
Butler groups formed by factoring a completely decomposable group by a rank one group have been studied extensively. We call such groups, bracket groups. We study bracket modules over integral domains. In particular, we are interested in when any bracket -module is tensor a bracket group.
Using the notion of cyclically pure injective modules, a characterization of rings which are locally valuation rings is established. As applications, new characterizations of Prüfer domains and pure semisimple rings are provided. Namely, we show that a domain R is Prüfer if and only if two of the three classes of pure injective, cyclically pure injective and RD-injective modules are equal. Also, we prove that a commutative ring R is pure semisimple if and only if every R-module is cyclically pure...
Currently displaying 1 –
20 of
170