Forcing Linearity Numbers

✍ Scribed by C.J. Maxson; J.H. Meyer

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 170 KB
• Volume: 223
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.7991

✦ Synopsis

For a module over a ring R we introduce the concept of a forcing linearity number which is a type of measure of how much local linearity is needed to imply global linearity. We determine this number for vector spaces, for modules over integral domains, not fields, and for modules over local rings, not integral domains. © 2000 Academic Press

1. Introduction

Throughout this paper we let R denote a ring with identity and V a unital (left) R-module and consider the set

Under the operations of function addition and composition of maps, M R V is a near-ring called the near-ring of homogeneous functions on V . Note that M R V contains End R V , the ring of R-endomorphisms of V . Recent investigations have considered the problem of how much local linearity is needed on a function f ∈ M R V to 190