The Ohio University and Ohio State University Ring Theory Seminar presents Jae Keol Park on “Compatible ring structures on injective hulls – Revisited” on Friday, Nov. 7, at 4:45 p.m. in Cockins Hall 240, in the Department of Mathematics at OSU.
Park is from Pusan National University in Busan, South Korea.
Abstract: Let R be a ring and E(R_R) be an injective hull of R_R. A ring structure on E(R_R) is said to be compatible if the ring multiplication on E(R_R) is an extension of the R-module scalar multiplication of E(R_R) over R. In this talk, we discuss compatible ring structures on an injective hull E(R_R) of R_R. If E(R_R) has a compatible ring structure (E(R_R), +, \cdot), then we provide a way of constructing another compatible ring structure on E(R_R), when E(R_R) is not a rational extension of R_R. Furthermore, if R and S are two isomorphic rings, then we can show that E(R_R) has $\aleph$ distinct compatible ring structures if and only if E(S_S) has $\aleph$ distinct compatible ring structures, where $\aleph$ is a cardinal number. We will also discuss some related examples. (This is a joint work with Tariq Rizvi).
Upcoming Events
Yuval Ginosar of University of Haifa (Israel) will be the Ring Theory speaker for two seminars in mid-November.
On Thursday, Nov. 13, he will give a talk on “Semi-invariant matrices” at Ohio University in Morton from 4 to 5 p.m.
Abstract: The semi-invariants of a module-algebra over a group G are the elements in its 1-dimensional constituents. These elements span a subalgebra, called the semi-center, which is graded by the linear characters of G. By studying the projective representations of G, we describe the semi-center of matrix algebras, or more generally of artinian semi-simple G-module-algebras. This is joint work with O. Schnabel.
On Friday, Nov. 14, he will speak on “Isotropy in group cohomology” at Ohio State University at 4:45 p.m.
Abstract: The analog of Lagrangians for symplectic forms over finite groups is motivated by the fact that symplectic G-forms with a normal Lagrangian N are in one-to-one correspondence, up to inflation, with bijective 1-cocycle data on the quotients G/N. This yields a method to construct groups of central type from such quotients, known as Involutive Yang-Baxter groups. Based on joint works with N. Ben David and E. Meir.
Comments