The aim of this article is to study the
ring associated to a Koszul
-ring and to use it to provide further characterisations of the latter. As such, for
being a semisimple ring and
a graded Koszul
-ring, we will prove that there is an isomorphism of DG rings between
. Also, the
-ring will prove to be isomorphic to the shriek ring of the left graded dual of
. As an application, these isomorphisms will be studied in the context of incidence
-(co)rings for Koszul posets. Thus, we will obtain a description and method of computing the shriek ring for K
, the incidence
-coring of a Koszul poset. Another application is provided for monoid rings associated to submonoids of
Key Words: Koszul rings, Koszul corings, Koszul pairs, ring.
2000 Mathematics Subject Classification: Primary: 16E40;
Secondary: 16T15, 16E30.