Coproduct of crossed A-modules of R-algebroids

AVCIOĞLU O., AKÇA İ. İ.

Topological Algebra and its Applications, vol.5, no.1, pp.37-48, 2017 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.1515/taa-2017-0007
  • Journal Name: Topological Algebra and its Applications
  • Journal Indexes: Scopus
  • Page Numbers: pp.37-48
  • Keywords: Algebroid, Coproduct, Crossed module, Free product, Semidirect product
  • Uşak University Affiliated: Yes

Abstract

In this study we construct, in the category XAlg(R)/A of crossed A-modules of R-algebroids, the coproduct of given two crossed A-modules M = (µ : M −→ A) and N = (η : N −→ A) of R-algebroids in two different ways: Firstly we construct the coproduct M ◦* N by using the free product M * N of pre-R-algebroids M and N, and then we construct the coproduct M ◦n N by using the semidirect product M n N of M and N via µ. Finally we construct an isomorphism between M ◦* N and M ◦n N.