Injective and projective semimodules over involutive semirings

Idempotent Subreducts of Semimodules over Commutative Semirings

A short proof of the characterization of idempotent subreducts of semimodules over commutative semirings is presented. It says that an idempotent algebra embeds into a semimodule over a commutative semiring, if and only if it belongs to the variety of Szendrei modes.

Further Galois Connections between Semimodules over Idempotent Semirings

In [14] a generalisation of Formal Concept Analysis was introduced with data mining applications in mind, K-Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the standard Boolean carrier set. The construction leading to the pair of dually (order) isomorphic lattices can be further manipulated to obtain the three other types of Galois Connections pro...

CHARACTERIZATIONS OF PROJECTIVE AND k-PROJECTIVE SEMIMODULES

$mathcal{X}$-injective and $mathcal{X}$-projective complexes

Let $mathcal{X}$ be a class of $R$-modules‎. ‎In this paper‎, ‎we investigate ;$mathcal{X}$-injective (projective) and DG-$mathcal{X}$-injective (projective) complexes which are generalizations of injective (projective) and DG-injecti‎‎ve (projective) complexes‎. ‎We prove that some known results can be extended to the class of ;$mathcal{X}$-injective (projective) and DG-$mathcal{X}$-injective ...

Strongly Gorenstein projective , injective and flat modules

Let R be a ring and n a fixed positive integer, we investigate the properties of n-strongly Gorenstein projective, injective and flat modules. Using the homological theory , we prove that the tensor product of an n-strongly Gorenstein projective (flat) right R -module and projective (flat) left R-module is also n-strongly Gorenstein projective (flat). Let R be a coherent ring ,we prove that the...