On zero subrings and periodic subrings.
On -singular and -extending modules
Let be a module and be a class of modules in which is closed under isomorphisms and submodules. As a generalization of essential submodules Özcan in [8] defines a -essential submodule provided it has a non-zero intersection with any non-zero submodule in . We define and investigate -singular modules. We also introduce -extending and weakly -extending modules and mainly study weakly -extending modules. We give some characterizations of -co-H-rings by weakly -extending modules. Let ...
Ordered ultraconnected rings
Ordinary selfdistributive rings
Left selfdistributive rings (i.e., ) which are semidirect sums of boolean rings and rings nilpotent of index at most 3 are studied.
Orthodox bands of modules
-clean rings.
Periodic rings with commuting nilpotents.
Periodic rings with finitely generated underlying group.
Phantom maps and purity in modular representation theory, I
Let k be a field and G a finite group. By analogy with the theory of phantom maps in topology, a map f : M → ℕ between kG-modules is said to be phantom if its restriction to every finitely generated submodule of M factors through a projective module. We investigate the relationships between the theory of phantom maps, the algebraic theory of purity, and Rickard's idempotent modules. In general, adding one to the pure global dimension of kG gives an upper bound for the number of phantoms we need...
Preprojective Components of Wild Tilted Algebras.
Preradicals
Preradicals and change of rings
Primary decomposition of torsion -modules.
Prime modules.
Primitive Ideals of Certain Noetherian Algebras.
ℵ-products of modules and splitness.
Let0 → ∏ℵI Mα ⎯λ→ ∏I Mα ⎯γ→ Coker λ → 0 be an exact sequence of modules, in which ℵ is an infinite cardinal, λ the natural injection and γ the natural surjection. In this paper, the conditions are given mainly in the four theorems so that λ (γ respectively) is split or locally split. Consequently, some known results are generalized. In particular, Theorem 1 of [7] and Theorem 1.6 of [5] are improved.
Products of small modules
Module is said to be small if it is not a union of strictly increasing infinite countable chain of submodules. We show that the class of all small modules over self-injective purely infinite ring is closed under direct products whenever there exists no strongly inaccessible cardinal.
Projektive Moduln mit endlich erzeugtem Radialfaktormodul.
Properties of slender rings.
Propriétés d'unicité des supplémentaires