It has also been adapted in abstract algebra courses in several other distinguished universities across China. The aim of this book is to introduce the fundamental theories of groups, rings, modules, ...

This package provides a Coq formalization of abstract algebra using a functional programming style. The modules contained within the package span monoids, groups, rings, and fields and provides both ...

Abstract: Many graph query languages rely on composition to navigate graphs and select nodes of interest, even though evaluating compositions of relations can be costly. Often, this need for ...

Abstract: In this paper, the construction of semi-algebra Low-density parity-check (LDPC) code with an arbitrary block length is presented. The encoding circuit is based on the original semi-algebra ...

Algebraic structures such as semirings and modules have long been a fertile ground for both theoretical exploration and practical application. Semirings, generalisations of rings that typically ...

ABSTRACT: In this article, we introduce the notion of fuzzy G-module by defining the group action of G on a fuzzy set of a Z-module M. We establish the cases in which fuzzy submodules also become ...