International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2001 / Article

Open Access

Volume 27 |Article ID 820493 | https://doi.org/10.1155/S0161171201000849

Yasien Gh. Gouda, "Reflexive and dihedral (co)homology of a pre-additive category", International Journal of Mathematics and Mathematical Sciences, vol. 27, Article ID 820493, 10 pages, 2001. https://doi.org/10.1155/S0161171201000849

Reflexive and dihedral (co)homology of a pre-additive category

Received18 Jun 1998

Abstract

The group dihedral homology of an algebra over a field with characteristic zero was introduced by Tsygan (1983). The dihedral homology and cohomology of an algebra with involution over commutative ring with identity, associated with the small category, were studied by Krasauskas et al. (1988), Loday (1987), and Lodder (1993). The aim of this work is concerned with dihedral and reflexive (co)homology of small pre-additive category. We also define the free product of involutive algebras associated with this category and study its dihedral homology group. Finally, following Perelygin (1990), we show that a small pre-additive category is Morita equivalence.

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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