Good Gradings of Generalized Incidence Rings
Kenneth L. Price
TL;DR
This paper explores conditions under which generalized incidence rings can be isomorphically graded to subrings of incidence rings over preorders and extends existing grading constructions to broader cases.
Contribution
It provides new conditions for graded isomorphisms of generalized incidence rings and extends group grading constructions to more complex preorders.
Findings
Conditions for graded isomorphism to incidence rings over preorders
Extension of group grading constructions to preorders with short crosscuts
Broader applicability of good group gradings in incidence algebras
Abstract
This inquiry is based on both the construction of generalized incidence rings due to Gene Abrams and the construction of good group gradings of incidence algebras due to Molli Jones. We provide conditions for a generalized incidence ring to be graded isomorphic to a subring of an incidence ring over a preorder. We also extend Jones's construction to good group gradings for incidence algebras over preorders with crosscuts of length one or two.
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Taxonomy
TopicsRings, Modules, and Algebras · Algebraic structures and combinatorial models · Advanced Topics in Algebra