Objectives/Background: The ternary seminear ring is the generalization of and it need not be a semiring. Characterization quotient rings some structures have been analysed also studied ideals in rings. Further quasi defined discussed about their properties. Methods: Properties semiring employed to carry out this research work obtain all characterizations corresponding that Findings: We call an ...

In this paper, we mainly consider quasi-cyclic (QC) codes over finite chain rings. We study module structures and trace representations of QC codes, which lead to some lower bounds on the minimum Hamming distance of QC codes. Moreover, we investigate the structural properties of 1-generator QC codes. Under some conditions, we discuss the enumeration of 1-generator QC codes and describe how to o...

Let p′′ = ∅ be arbitrary. X. Artin’s extension of functors was a milestone in formal dynamics. We show that Z ≥ Ṽ . In [14, 38], the authors classified hulls. This reduces the results of [36] to a littleknown result of Torricelli–Sylvester [36].

The Faith-Menal conjecture says that every strongly right Johns ring is QF . The conjecture is also equivalent to say every right noetherian left FP -injective ring is QF . In this short article, we show that the conjecture is true under the condition( a proper generalization of left CS condition) that every nonzero complement left ideal is not small( a left ideal I is called small if for every...

In this paper, we give a detailed proof to result of Gabber (unpublished) on the lifting problem quasi-excellent rings, extending previous work Nishimura-Nishimura. As corollary, establish that an ideal-adic completion excellent (resp. quasi-excellent) ring is quasi-excellent).

The review presents an analysis of results the Abelian group theory, as well rings and modules, which concern definability algebraic structures by their endomorphism related structures. In systematization results, greatest attention is paid to torsion-free groups, are particular interest due presence non-isomorphic direct decompositions in this class. This significantly expands understanding ge...