CHARACTERIZATION OF PRIME SUBMODULES OF A FREE MODULE OF FINITE RANK OVER A VALUATION DOMAIN
CHARACTERIZATION OF PRIME SUBMODULES OF A FREE MODULE OF FINITE RANK OVER A VALUATION DOMAIN
Let <TEX>$F=R^{(n)}$</TEX> be a free R-module of finite rank <TEX>$n{\geq}2$</TEX>. In this paper, we characterize the prime submodules of F with at most n generators when R is a <TEX>$Pr{\ddot{u}}fer$</TEX> domain. We also introduce the notion of prime matrix and we show that when R is a valuation domain, every …