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*-Derivations on Gamma-semihyperrings
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Introducing a pseudo-inverse with a specific condition on a $\Gamma $-semihyperring transforms it into an MA-$\Gamma $-semihyperring. We
introduce the notion of MA-$\Gamma $-semihyperring to initiate the theory of
commutators in $\Gamma $-semihyperrings. An additive mapping holding the
Leibniz rule is known as a derivation. Concepts of $\star $-derivation, $\star $-$f$-derivation, reverse $\star $-$f$-derivation, hermitian element,
and skew commutativeness on MA-$\Gamma $-semihyperrings endowed with an
involution are introduced, and various results pertaining to these concepts
are established. Moreover, an application of $\star $-derivation and $\star f$-derivation is demonstrated through certain constraints in determining
whether the MA-$\Gamma $-semihyperring exhibits skew or weak commutativity.
Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine
Title: *-Derivations on Gamma-semihyperrings
Description:
Introducing a pseudo-inverse with a specific condition on a $\Gamma $-semihyperring transforms it into an MA-$\Gamma $-semihyperring.
We
introduce the notion of MA-$\Gamma $-semihyperring to initiate the theory of
commutators in $\Gamma $-semihyperrings.
An additive mapping holding the
Leibniz rule is known as a derivation.
Concepts of $\star $-derivation, $\star $-$f$-derivation, reverse $\star $-$f$-derivation, hermitian element,
and skew commutativeness on MA-$\Gamma $-semihyperrings endowed with an
involution are introduced, and various results pertaining to these concepts
are established.
Moreover, an application of $\star $-derivation and $\star f$-derivation is demonstrated through certain constraints in determining
whether the MA-$\Gamma $-semihyperring exhibits skew or weak commutativity.
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