A note on orthodox additive inverse semirings

M. K. Sen; S. K. Maity

Displaying similar documents to “A note on orthodox additive inverse semirings”

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.

On sandwich sets and congruences on regular semigroups

Mario Petrich (2006)

Czechoslovak Mathematical Journal

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Let $S$ be a regular semigroup and $E (S)$ be the set of its idempotents. We call the sets $S (e, f) f$ and $e S (e, f)$ one-sided sandwich sets and characterize them abstractly where $e, f \in E (S)$ . For $a, a^{'} \in S$ such that $a = a a^{'} a$ , $a^{'} = a^{'} a a^{'}$ , we call $S (a) = S (a^{'} a, a a^{'})$ the sandwich set of $a$ . We characterize regular semigroups $S$ in which all $S (e, f)$ (or all $S (a))$ are right zero semigroups (respectively are trivial) in several ways including weak versions of compatibility of the natural order. For every $a \in S$ , we also define $E (a)$ as the set of all idempotets $e$ such that, for any congruence...

Inverse semirings whose additive endomorphisms are multiplicative

Bedřich Pondělíček (1996)

Mathematica Slovaca

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Differentiability of the g-Drazin inverse

J. J. Koliha, V. Rakočević (2005)

Studia Mathematica

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If A(z) is a function of a real or complex variable with values in the space B(X) of all bounded linear operators on a Banach space X with each A(z)g-Drazin invertible, we study conditions under which the g-Drazin inverse $A^{} (z)$ is differentiable. From our results we recover a theorem due to Campbell on the differentiability of the Drazin inverse of a matrix-valued function and a result on differentiation of the Moore-Penrose inverse in Hilbert spaces.