Primary decomposition in a soft ring and a soft module

Document Type: Regular Paper

Authors

Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

Abstract

The main objective of this study is to swing Krull intersection theorem in primary decomposition of rings and
modules to the primary decomposition of soft rings and soft modules. To fulfill this aim several notions like soft
prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a
given unitary commutative ring. Consequently, the primary decomposition of soft rings and soft modules is
established. In addition, the ascending and descending chain conditions on soft ideals and soft sub modules of soft
rings and soft modules are introduced, respectively, enabling us to develop the notions of soft Noetherian rings
and soft Noetherian modules.

Keywords