Associated Prime Ideals in Commutative Algebra

Abstract

This paper aims to explain how an abstract mathematical object of higher mathematics is learnt and solved the given problem from the pedagogical perspectives resting the explanation based upon the solution of higher mathematical problem in abstract algebra.The purpose is not only to disseminate the solution of the problem but to unfold the learning realities in course of pursuing the pure discovery learning path. The problem of the study was connected to the understandings of associated prime ideals in commutative algebra. Factual materials including books, lecture notes and research articles were used to explore the concepts on associated prime ideals. The concepts learned were summarized, conceptualized, and then analyzed together with established facts of algebraic concepts and developed examples to interpret the abstract concepts: the associated prime ideals. The associated prime ideal was explored and understood within the conceptions of primary decomposition, Noetherian rings, and modules, and then characterized some fundamental notions of it on an A-module M over the Noetherian ring A. The results reveal that repeated reading, writing, rigorous thinking and linking, and engaging on abstraction are the basic characteristics of content researcher in developing and constructing new insights, ideas and knowledge in higher mathematics from pedagogic perspective