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BIPROJECTIVITY AND BIFLATNESS OF LAU PRODUCT OF BANACH ALGEBRAS DEFINED BY A BANACH ALGEBRA MORPHISM

Part of: Topological algebras, normed rings and algebras, Banach algebras Methods of category theory in functional analysis

Published online by Cambridge University Press:  15 July 2014

F. ABTAHI ,
A. GHAFARPANAH  and
A. REJALI
F. ABTAHI*
Affiliation:
Department of Mathematics, University of Isfahan, PO Box 81746-73441, Isfahan, Iran email f.abtahi@sci.ui.ac.ir, abtahif2002@yahoo.com
A. GHAFARPANAH
Affiliation:
Department of Mathematics, University of Isfahan, PO Box 81746-73441, Isfahan, Iran email ghafarpanah@sci.ui.ac.ir, ghafarpanah1393@gmail.com
A. REJALI
Affiliation:
Department of Mathematics, University of Isfahan, PO Box 81746-73441, Isfahan, Iran email rejali@sci.ui.ac.ir, alirejali12@gmail.com
*
✉abtahi.fatemeh@yahoo.com
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Abstract

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Let ${\it\varphi}$ be a homomorphism from a Banach algebra ${\mathcal{B}}$ to a Banach algebra ${\mathcal{A}}$. We define a multiplication on the Cartesian product space ${\mathcal{A}}\times {\mathcal{B}}$ and obtain a new Banach algebra ${\mathcal{A}}\times _{{\it\varphi}}{\mathcal{B}}$. We show that biprojectivity as well as biflatness of ${\mathcal{A}}\times _{{\it\varphi}}{\mathcal{B}}$ are stable with respect to ${\it\varphi}$.

Keywords

biflatnessbiprojectivitybimodule map𝜃-Lau product

MSC classification

Primary: 46M10: Projective and injective objects
Secondary: 46H25: Normed modules and Banach modules, topological modules (if not placed in or ) 46M18: Homological methods (exact sequences, right inverses, lifting, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 1 , February 2015 , pp. 134 - 144
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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