Standard bases for modules over polynomial subalgebras. Issue 1 (23rd July 2020)

• Record Type: Journal Article
• Authors: Kanwal, Nazish; Jabeen, Nazia; Khan, Junaid Alam
• Is Part Of: Communications in algebra. Volume 49:Issue 1(2021)
• Page Start: 58
• Page End: 72
• Publication Date: 2020-07-23
• Subjects: Degree maps -- grading -- Gröbner bases -- H-bases; 13P10; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1793160
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: In this article, we present the theory of standard bases for modules over polynomial subalgebras based on arbitrary gradings (induced by an additive monoid Γ) which we called SΓ-bases. This paper deals with the problem of construction of SΓ-bases for submodules of free module over polynomial subalgebras. For this purpose, we present an algorithm based on SΓ-normal form and discuss it for some special gradings.