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On centralizers of semiprime rings with involution
Studia Scientiarum Mathematicarum Hungarica, 2006LetRbe a 2-torsion free semiprime *-ring and letT:R?Rbe an additive mapping such thatT(xx*)=T(x)x* is fulfilled for allx?R. In this caseT(xy)=T(x)yholds for all pairsx,y?R.
Joso Vukman, Irena Kosi-Ulbl
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HIGHER DERIVATIONS OF SEMIPRIME RINGS
Communications in Algebra, 2002ABSTRACT In this paper we study higher derivations of prime and semiprime rings satisfying linear relations. We extend several results known for algebraic derivations, and we prove some other results.
Claus Haetinger, Miguel Ferrero
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On Jordan Structure in Semiprime Rings
Canadian Journal of Mathematics, 1976A remarkable theorem of Herstein [1, Theorem 2] of which we have made several uses states: If R is a semiprime ring of characteristic different from 2 and if U is both a Lie ideal and a subring of R then either U ⊂ Z (the centre of R) or U contains a nonzero ideal of R. In a recent paper [3] Herstein extends the above mentioned result significantly and
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1973
A ring S is a (classical) right quotient ring of a subring T if every regular element a ∈ T has an inverse in S and $$ S = \{ a{b^{ - 1}}|a,b \in T,b\;{\text{reular}}\} $$ Then T is an order in S (cf. 7.21). The following condition is necessary and sufficient for a ring T to possess a classical quotient ring: If a, b ∈ T, and if b is regular ...
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A ring S is a (classical) right quotient ring of a subring T if every regular element a ∈ T has an inverse in S and $$ S = \{ a{b^{ - 1}}|a,b \in T,b\;{\text{reular}}\} $$ Then T is an order in S (cf. 7.21). The following condition is necessary and sufficient for a ring T to possess a classical quotient ring: If a, b ∈ T, and if b is regular ...
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THE SEMIPRIMENESS OF SEMIGROUP RINGS
JP Journal of Algebra, Number Theory and Applications, 2021Yasuyuki Hirano +2 more
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, 1990