Page 1 Next

Displaying 1 – 20 of 168

Showing per page

( δ , 2 ) -primary ideals of a commutative ring

Gülşen Ulucak, Ece Yetkin Çelikel (2020)

Czechoslovak Mathematical Journal

Let R be a commutative ring with nonzero identity, let ( ) be the set of all ideals of R and δ : ( ) ( ) an expansion of ideals of R defined by I δ ( I ) . We introduce the concept of ( δ , 2 ) -primary ideals in commutative rings. A proper ideal I of R is called a ( δ , 2 ) -primary ideal if whenever a , b R and a b I , then a 2 I or b 2 δ ( I ) . Our purpose is to extend the concept of 2 -ideals to ( δ , 2 ) -primary ideals of commutative rings. Then we investigate the basic properties of ( δ , 2 ) -primary ideals and also discuss the relations among ( δ , 2 ) -primary, δ -primary and...

A class of multiplicative lattices

Tiberiu Dumitrescu, Mihai Epure (2021)

Czechoslovak Mathematical Journal

We study the multiplicative lattices L which satisfy the condition a = ( a : ( a : b ) ) ( a : b ) for all a , b L . 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 L localized at its maximal elements are totally ordered sharp lattices. The converse is true if L has finite character.

A class of torsion-free abelian groups characterized by the ranks of their socles

Ulrich F. Albrecht, Anthony Giovannitti, H. Pat Goeters (2002)

Czechoslovak Mathematical Journal

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 R -module is R tensor a bracket group.

A criterion for rings which are locally valuation rings

Kamran Divaani-Aazar, Mohammad Ali Esmkhani, Massoud Tousi (2009)

Colloquium Mathematicae

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 168

Page 1 Next