0000000000403161
AUTHOR
Pedro Patrício
The diamond partial order in rings
In this paper we introduce a new partial order on a ring, namely the diamond partial order. This order is an extension of a partial order defined in a matrix setting in [J.K. Baksalary and J. Hauke, A further algebraic version of Cochran's theorem and matrix partial orderings, Linear Algebra and its Applications, 127, 157--169, 1990]. We characterize the diamond partial order on rings and study its relationships with other partial orders known in the literature. We also analyze successors, predecessors and maximal elements under the diamond order.
Special elements in a ring related to Drazin inverses
In this paper, the existence of the Drazin (group) inverse of an element a in a ring is analyzed when amk = kan, for some unit k and m; n 2 N. The same problem is studied for the case when a* = kamk-1 and for the fk; s+1g-potent elements. In addition, relationships with other special elements of the ring are also obtained