The tensor product of function algebras
Youssef Azouzi, Mohamed Amine Ben Amor, Jamel Jaber
TL;DR
This paper investigates the tensor product of two $f$-algebras, demonstrating that their Riesz tensor product naturally inherits an $f$-algebra structure, thus advancing the understanding of algebraic tensor products in ordered algebraic systems.
Contribution
It proves that the Riesz tensor product of two $f$-algebras forms an $f$-algebra, establishing a new structural result in the theory of ordered algebraic tensor products.
Findings
The Riesz subspace generated by a subalgebra in an $f$-algebra is itself an algebra.
The Riesz tensor product of two $f$-algebras has an $f$-algebra structure.
Abstract
In this paper we study the tensor product of two -algebras. We show that the Riesz Subspace generated by a subalgebra in an -algebra is an algebra in order to prove that the Riesz tensor product of two -algebras has a structure of an -algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Banach Space Theory