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 generalizations of injectivity.
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 formal power series
On generalized gamma near-fields.
On generalized Jordan derivations of Lie triple systems
Under some conditions we prove that every generalized Jordan triple derivation on a Lie triple system is a generalized derivation. Specially, we conclude that every Jordan triple -derivation on a Lie triple system is a -derivation.
On generalized partial twisted smash products
We first introduce the notion of a right generalized partial smash product and explore some properties of such partial smash product, and consider some examples. Furthermore, we introduce the notion of a generalized partial twisted smash product and discuss a necessary condition under which such partial smash product forms a Hopf algebra. Based on these notions and properties, we construct a Morita context for partial coactions of a co-Frobenius Hopf algebra.
On generalized periodic-like rings.
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 quaternion algebras.
On Generalized Regular Rings.
On Generalized Subcommutative Regular Rings.
On Generalized Uniserial Rings and Decompositions that Complement Direct Summands.
On generalized -derivations.
On Gorenstein flat preenvelopes of complexes
On Gorenstein Rings.
On graded algebra bundles.
On graph associated to co-ideals of commutative semirings
Let be a commutative semiring with non-zero identity. In this paper, we introduce and study the graph whose vertices are all elements of and two distinct vertices and are adjacent if and only if the product of the co-ideals generated by and is . Also, we study the interplay between the graph-theoretic properties of this graph and some algebraic properties of semirings. Finally, we present some relationships between the zero-divisor graph and .
On graphs associated to rings.