Unit exchange elements in rings

Grigore Calugareanu

Abstract


Replacing left principal ideals by cosets in the monoid (R, ·) of a unital
ring R, we say that an element a 2 R is left unit exchange (or suitable)
if there is an idempotent e 2 R such that e − a 2 U(R)(a − a2) where
U(R) denotes the set of units. Unit-regular and clean elements are left
(and right) unit suitable, and left (or right) unit suitable elements are
exchange (suitable).
The paper studies the multiple facets of this new notion.

Keywords


clean element; unit- regular element; exchange (suitable) element; unit suitable element; matrix rings

Full Text:

PDF

References


D. Andrica, G. C˘alug˘areanu A nil-clean 2 x 2 matrix over integers which is not clean. J. of Algebra and its Applications, 13 (6) (2014), 9 pages.

G. C˘alug˘areanu Split-extensions of Exchange Rings: a direct proof. J. of

Algebra and Applications 8 (5) (2009), 629-632.

D. Khurana, T. Y. Lam Clean matrices and unit-regular matrices. J. of

Algebra 280 (2004), 683-698.

T. Y. Lam, P. Nielsen Jacobson’s lemma for Drazin inverses. In Ring Theoory and its Appl., Contemporary Math. 609 (2014), 185-196.

W. K. Nicholson Lifting idempotents and exchange rings. Trans. A.M.S. 229 (1977), 269-278.

J.ˇ Ster Corner rings of a clean ring need not be clean. Comm. Algebra 40 (5) (2012),1595-1604.

J.ˇ Ster Weakly clean rings. J of Algebra 401 (2014), 1-12.




DOI: http://dx.doi.org/10.24193/subbmath.2020.3.02

Refbacks

  • There are currently no refbacks.