A note on orthodox additive inverse semirings

M. K. Sen; S. K. Maity

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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)

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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.

Inverse zero-sum problems {II}

Wolfgang A. Schmid (2010)

Acta Arithmetica

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Orthodox $Γ$ -semigroups.

Sen, M.K., Saha, N.K. (1990)

International Journal of Mathematics and Mathematical Sciences

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On Meager Additive and Null Additive Sets in the Cantor Space $2^{ω}$ and in ℝ

Tomasz Weiss (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let T be the standard Cantor-Lebesgue function that maps the Cantor space $2^{ω}$ onto the unit interval ⟨0,1⟩. We prove within ZFC that for every $X \subseteq 2^{ω}$ , X is meager additive in $2^{ω}$ iff T(X) is meager additive in ⟨0,1⟩. As a consequence, we deduce that the cartesian product of meager additive sets in ℝ remains meager additive in ℝ × ℝ. In this note, we also study the relationship between null additive sets in $2^{ω}$ and ℝ.

On centralizer of semiprime inverse semiring

S. Sara, M. Aslam, M.A. Javed (2016)

Discussiones Mathematicae General Algebra and Applications

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Let S be 2-torsion free semiprime inverse semiring satisfying A₂ condition of Bandlet and Petrich [1]. We investigate, when an additive mapping T on S becomes centralizer.