Displaying similar documents to “One-sided complements and solutions of the equation a X b = c in semirings.”

On generalized inverses in C*-algebras

Robin Harte, Mostafa Mbekhta (1992)

Studia Mathematica

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We investigate when a C*-algebra element generates a closed ideal, and discuss Moore-Penrose and commuting generalized inverses.

On the Drazin index of regular elements

Pedro Patrício, António Costa (2009)

Open Mathematics

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It is known that the existence of the group inverse a # of a ring element a is equivalent to the invertibility of a 2 a − + 1 − aa −, independently of the choice of the von Neumann inverse a − of a. In this paper, we relate the Drazin index of a to the Drazin index of a 2 a − + 1 − aa −. We give an alternative characterization when considering matrices over an algebraically closed field. We close with some questions and remarks.

Semirings embedded in a completely regular semiring

M. K. Sen, S. K. Maity (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Recently, we have shown that a semiring S is completely regular if and only if S is a union of skew-rings. In this paper we show that a semiring S satisfying a 2 = n a can be embedded in a completely regular semiring if and only if S is additive separative.

Multiplicatively idempotent semirings

Ivan Chajda, Helmut Länger, Filip Švrček (2015)

Mathematica Bohemica

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Semirings are modifications of unitary rings where the additive reduct does not form a group in general, but only a monoid. We characterize multiplicatively idempotent semirings and Boolean rings as semirings satisfying particular identities. Further, we work with varieties of enriched semirings. We show that the variety of enriched multiplicatively idempotent semirings differs from the join of the variety of enriched unitary Boolean rings and the variety of enriched bounded distributive...