Year: 2012
Type: preprint
Abstract: In this paper we present the definition of quasi-bases for modules over a ring that is commutative but not necessarily division and discuss properties that guarantee the existence of quasi-bases. Based on this result we further prove that every finitely generated module over $L^{0}(\mathcal{F},K)$ has a quasi-basis, where $K$ is the scalar field of real numbers or complex numbers and $L^{0}(\mathcal{F},K)$ is the algebra of equivalence classes of $K$--valued random variables defined on a probability space $(Ω,\mathcal{F},P)$.
Source: arXiv (Cornell University)
Author: Shi, Guang
Institution: Beihang University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1640129909