Cain, Jessica G.; Frauendienst, Leah R.; Veerapen, Padmini A notion of rank for noncommutative quadratic forms on four generators. (English) Zbl 1517.16025 J. Algebra Appl. 21, No. 10, Article ID 2250196, 17 p. (2022). Summary: In this paper, we extend work from [M. Vancliff and P. P. Veerapen, Contemp. Math. 592, 241–250 (2013; Zbl 1326.16019)], where a notion of rank, called \(\mu\)-rank, was proposed for noncommutative quadratic forms on two and three generators. In particular, we provide a definition of \(\mu\)-rank one and two for noncommutative quadratic forms on four generators. We apply this definition to determine the number of point modules over certain quadratic AS-regular algebras of global dimension four. MSC: 16S36 Ordinary and skew polynomial rings and semigroup rings 15A63 Quadratic and bilinear forms, inner products 15A03 Vector spaces, linear dependence, rank, lineability Keywords:quadratic form; rank; skew polynomial ring; \(\mu\)-symmetric matrix Citations:Zbl 1326.16019 PDFBibTeX XMLCite \textit{J. G. Cain} et al., J. Algebra Appl. 21, No. 10, Article ID 2250196, 17 p. (2022; Zbl 1517.16025) Full Text: DOI arXiv References: [1] Artin, M., Tate, J. and Van den Bergh, M., Some algebras associated to automorphisms of elliptic curves, in The Grothendieck Festschrift, Vol. 1, eds. Cartier, P.et al., (Birkhäuser, Boston, 1990), pp. 33-85. · Zbl 0744.14024 [2] Artin, M., Tate, J. and Van den Bergh, M., Modules over regular algebras of dimension 3, Invent. Math.106 (1991) 335-388. · Zbl 0763.14001 [3] Cassidy, T. and Vancliff, M., Generalizations of graded Clifford algebras and of complete intersections, J. Lond. Math. Soc.81 (2010) 91-112. · Zbl 1236.16026 [4] Stephenson, D. R. and Vancliff, M., Constructing Clifford quantum \(\Bbb P^3\) s with finitely many points, J. Algebra312(1) (2007) 86-110. · Zbl 1130.15020 [5] M. Vancliff and P. P. Veerapen, Generalizing the notion of rank to noncommutative quadratic forms, in Noncommutative Birational Geometry, Representations and Combinatorics, eds. A. Berenstein and V. Retakh, Contemporary Mathematics, Vol. 592 (2013), pp. 241-250. · Zbl 1326.16019 [6] Vancliff, M. and Veerapen, P. P., Point modules over graded skew Clifford algebras, J. Algebra420 (2014) 54-64. · Zbl 1332.16021 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.