Add to ORKGA coalgebra C is said to have the splitting property if the maximal rational submodule Rat(M) of any left C∗-module M is a direct sum-mand of it. In this paper we prove that a coalgebra C satisfying this property is finite dimensional. Cocommutative coalgebras such that Rat(M) is a direct summand for any finitely generated left C∗-module M are explicitly described
For an arbitrary-type functor F, the notion of split coalgebras, that is, coalgebras for which the c...
A right R-module M is called: (1) retractable if HomR(M,N)≠0 for any non-zero submodule N of M; (2) ...
AbstractThe notion of an endofunctor having “greatest subcoalgebras” is introduced as a form of comp...
AbstractLet R be a ring and let t be a torsion preradical, R is said to have the splitting property,...
AbstractLet A be a pseudocompact (or profinite) algebra, so A=C∗ where C is a coalgebra. We show tha...
A characterization is given of the finitely generated non-singular left i?-modules N such that Extβ ...
AbstractWe show that coalgebras whose lattice of right coideals is distributive are coproducts of co...
Given an endofunctor F of an arbitrary category, any maximal element of the lattice of congruence re...
Abstract We study rational modules over complete path and monomial algebras, and the problem of when...
AbstractLet R be a ring with identity. Let C be a class of R-modules which is closed under submodule...
AbstractIn this paper we extend the theory of serial and uniserial finite dimensional algebras to co...
An R-module V over a semiring R lacks zero sums (LZS) if x + y = 0 implies x = y = 0. More generally...
We study modules whose maximal submodules are supplements (direct summands). For a locally projectiv...
In this article we deal with modules with the property that all p-submodules are direct summands. In...
Because traditional ring theory places restrictive hypotheses on all submodules of a module, its res...
For an arbitrary-type functor F, the notion of split coalgebras, that is, coalgebras for which the c...
A right R-module M is called: (1) retractable if HomR(M,N)≠0 for any non-zero submodule N of M; (2) ...
AbstractThe notion of an endofunctor having “greatest subcoalgebras” is introduced as a form of comp...
AbstractLet R be a ring and let t be a torsion preradical, R is said to have the splitting property,...
AbstractLet A be a pseudocompact (or profinite) algebra, so A=C∗ where C is a coalgebra. We show tha...
A characterization is given of the finitely generated non-singular left i?-modules N such that Extβ ...
AbstractWe show that coalgebras whose lattice of right coideals is distributive are coproducts of co...
Given an endofunctor F of an arbitrary category, any maximal element of the lattice of congruence re...
Abstract We study rational modules over complete path and monomial algebras, and the problem of when...
AbstractLet R be a ring with identity. Let C be a class of R-modules which is closed under submodule...
AbstractIn this paper we extend the theory of serial and uniserial finite dimensional algebras to co...
An R-module V over a semiring R lacks zero sums (LZS) if x + y = 0 implies x = y = 0. More generally...
We study modules whose maximal submodules are supplements (direct summands). For a locally projectiv...
In this article we deal with modules with the property that all p-submodules are direct summands. In...
Because traditional ring theory places restrictive hypotheses on all submodules of a module, its res...
For an arbitrary-type functor F, the notion of split coalgebras, that is, coalgebras for which the c...
A right R-module M is called: (1) retractable if HomR(M,N)≠0 for any non-zero submodule N of M; (2) ...
AbstractThe notion of an endofunctor having “greatest subcoalgebras” is introduced as a form of comp...