On a class of semigroups admitting ring structure.
On a Substitution Property of Modules.
On algebras of strongly unbounded representation type.
On Anti-inverse Rings
On anti-inverse rings.
On biregular and regular rings
On countable von Neumann regular rings
On -rings
On essential left ideals of associative rings.
On generalization of injectivity
Characterizations of quasi-continuous modules and continuous modules are given. A non-trivial generalization of injectivity (distinct from -injectivity) is considered.
On generalized CS-modules
An -closed submodule of a module is a submodule for which is nonsingular. A module is called a generalized CS-module (or briefly, GCS-module) if any -closed submodule of is a direct summand of . Any homomorphic image of a GCS-module is also a GCS-module. Any direct sum of a singular (uniform) module and a semi-simple module is a GCS-module. All nonsingular right -modules are projective if and only if all right -modules are GCS-modules.
On generalized extending modules.
On generalized q.f.d. modules
A right -module is called a generalized q.f.d. module if every M-singular quotient has finitely generated socle. In this note we give several characterizations to this class of modules by means of weak injectivity, tightness, and weak tightness that generalizes the results in [sanh1], Theorem 3. In particular, it is shown that a module is g.q.f.d. iff every direct sum of -singular -injective modules in is weakly injective iff every direct sum of -singular weakly tight is weakly tight iff...
On Generalized Uniserial Rings and Decompositions that Complement Direct Summands.
On hereditary artinian rings and the pure semisimplicity conjecture: rigid tilting modules and a weak conjecture
A weak form of the pure semisimplicity conjecture is introduced and characterized through properties of matrices over division rings. The step from this weak conjecture to the full pure semisimplicity conjecture would be covered by proving that there do not exist counterexamples to the conjecture in a particular class of rings, which is also studied.
On hereditary rings and the pure semisimplicity conjecture II: Sporadic potential counterexamples
It was shown in [Colloq. Math. 135 (2014), 227-262] that the pure semisimplicity conjecture (briefly, pssC) can be split into two parts: first, a weak pssC that can be seen as a purely linear algebra condition, related to an embedding of division rings and properties of matrices over those rings; the second part is the assertion that the class of left pure semisimple sporadic rings (ibid.) is empty. In the present article, we characterize the class of left pure semisimple sporadic rings having finitely...
On infinite periodic rings.
On matrix rings over unit-regular rings.
On modules in which idempotent reducts form a chain
On modules with Le-decomposition.