Quadratic Forms and the ?-Invariant. II.
2000 Mathematics Subject Classification: 15A69, 15A78.In [3] we present the construction of the semi-symmetric algebra [χ](E) of a module E over a commutative ring K with unit, which generalizes the tensor algebra T(E), the symmetric algebra S(E), and the exterior algebra ∧(E), deduce some of its functorial properties, and prove a classification theorem. In the present paper we continue the study of the semi-symmetric algebra and discuss its graded dual, the corresponding canonical bilinear form,...
Assume that K is an arbitrary field. Let (I,⪯) be a poset of finite prinjective type and let KI be the incidence K-algebra of I. A classification of all sincere posets of finite prinjective type with three maximal elements is given in Theorem 2.1. A complete list of such posets consisting of 90 diagrams is presented in Tables 2.2. Moreover, given any sincere poset I of finite prinjective type with three maximal elements, a complete set of pairwise non-isomorphic sincere indecomposable prinjective...