Star operation on orders in simple Artinian rings

Abstract

Star operations are an important tool in multiplicative ideal theory. In this paper we apply a special type of star operation, known as $\nu$-operation, to define the notion of right Pr\"ufer $\nu$-multiplication order. The latter may be viewed as a natural non-commutative version of Pr\"ufer $\nu$-multiplication domain. As one of our main results, we establish that an overring of a right Pr\"ufer $\nu$-multiplication order is again a right Pr\"ufer $\nu$-multiplication order.