Higher Order mz-elements in Coherent Quantales

Abstract

The mz-elements of a coherent quantale have recently been defined by the author as an abstraction of the mz-ideals of a unital commutative ring. Having as its starting point the Dube and Ighedo recent paper on higher order ideals in ring theory, this paper deals with the higher order mz-elements of a coherent quantale A. For each natural number n we define the mz^n-elements of A, so we obtain an ascending sequence that covers the set of all higher order mz-elements. We obtain a lot of properties of this sequence. In particular, the stationarity of the sequence is studied. Another category of results investigates how the coherent quantale morphisms preserve such properties.

Keywords

• coherent quantales
• mz-elements
• mz^n-elements
• mzterminating quantale
• radically mz-covered quantale