Higher dimensional algebras as ideal maps

Odabaş A., Ulualan E.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.49, no.6, pp.1865-1884, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.15672/hujms.575080
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1865-1884
  • Keywords: crossed module, crossed square, ideal map, MODULES
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

In this work, we explain the close relationship between an ideal map structure S End(R)(R) on a homomorphism of commutative k-algebras R -> S and an ideal simplicial algebra structure on the associated bar construction Bar(S,R). We also explain this structure for crossed squares of algebras.