Toward an intuitive understanding of the structure of near-vector spaces. Issue 9 (2nd September 2022)

• Record Type: Journal Article
• Authors: Howell, K.-T.; Marques, S.
• Is Part Of: Communications in algebra. Volume 50:Issue 9(2022)
• Page Start: 3664
• Page End: 3677
• Publication Date: 2022-09-02
• Subjects: Near-vector spaces -- nearrings -- nearfields -- division rings -- span -- subspaces -- linear a + lgebra; 16Y30 -- 12K05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2022.2042543
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: In this article we analyze the definition André proposed for near-vector spaces to make it more transparent. We also study the class of near-vector spaces over division rings and give a characterization of regularity that gives a new insight into the decomposition of near-vector spaces into regular subspaces. We explicitly describe span and deduce a new characterization of subspaces.