Finite-dimensional lattice-ordered algebras with d-elements

Abstract

We first show that, under certain conditions, an -unital finite-dimensional Archimedean -algebra is isomorphic to a finite cyclic group -algebra with coefficients from a matrix -algebra. Then we characterize regular unital finite-dimensional Archimedean real -algebras which are either commutative or -reduced.  2004 Elsevier Inc. All rights reserved.

Lattice-ordered algebras with a d-basis

“…Therefore, as a totally ordered subfield of R, Q( √ 2) has no d-basis as an -algebra over the field Q of rational numbers. However, it has been shown in [10,Theorem 3.3] that if A is a finite-dimensional -algebra with a basis as a vector lattice over F , then A is regular if and only if A has a d-basis.…”