Algebra and Logic Seminar

The next meeting of the seminar will be held on October 6, 2017 (Friday), at 13:00, in Room 578 of the Institute of Mathematics and Informatics.

A talk on

UNIQUENESS IN VON NEUMANN REGULAR RINGS

will be delivered by Peter DANCHEV.

Everybody is invited.

Abstract. Forty years ago, Hartwig and Luh proved in (Pac. J. Math., 1977) that a unit-regular ring having unique inner inverse unit for each its element is either a boolean ring or a division ring, and vice versa. Extending their result, we define and explore certain other variations of uniquely elements in von Neumann regular rings. Specifically, we prove that a ring R is uniquely regular if, and only if, R is a division ring. We also show that a ring R is pseudo uniquely unit-regular if, and only if, R is a subdirect product of division rings.

These results are published in Palestine J. Math. (1) 7 (2018).