СЕМИНАР „АЛГЕБРА И ЛОГИКА”

Следващото заседание на семинара ще се проведе на 6 октомври 2017 г. (петък) от 13:00 часа в зала 578 на ИМИ – БАН.

Доклад на тема:

UNIQUENESS IN VON NEUMANN REGULAR RINGS

ще изнесе Петър Данчев.

Поканват се всички желаещи.

Резюме.  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).