On the Primary Decomposition of k-Ideals and Fuzzy k-Ideals in Semirings. Issue 2 (3rd April 2021)

• Record Type: Journal Article
• Authors: Sharma, Ram Parkash; Dadhwal, Madhu; Sharma, Richa; Kar, S.
• Is Part Of: Fuzzy information and engineering. Volume 13:Issue 2(2021)
• Page Start: 223
• Page End: 235
• Publication Date: 2021-04-03
• Subjects: Semirings -- fuzzy k-ideals -- primary ideals -- primary decomposition; 16Y60; Fuzzy systems -- Periodicals; Intelligent control systems -- Periodicals; 629.89
• DOI: 10.1080/16168658.2021.1950390
• Languages: English
• ISSNs: 1616-8658

Abstract

Abstract : Observing that every k -irreducible ideal of a semiring R is a k -primary ideal, if R is an additively cancellative, yoked and commutative Noetherian semiring, we establish the primary decomposition and uniqueness of the primary decomposition of k -ideals of such semirings. Finally, the primary decomposition and uniqueness of primary decomposition proved for k -ideals is also generalised for fuzzy k -ideals of these semirings.