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- W107540619 abstract "The aim of this note is to study properties of the generalized centroid of the semi-prime gamma rings. Main results are the following theorems: (1) Let M be a semi-prime <TEX>$Gamma$</TEX>-ring and Q a quotient <TEX>$Gamma$</TEX>-ring of M. If W is a non-zero submodule of the right (left) M-module Q, then <TEX>$WGamma$W</TEX> <TEX>$neq</TEX> 0. Furthermore Q is a semi-prime <TEX>$Gamma$</TEX>-ring. (2) Let M be a semi-prime <TEX>$Gamma$</TEX>-ring and <TEX>$C_{{Gamma}$</TEX> the generalized centroid of M. Then <TEX>$C_{Gamma}$</TEX> is a regular <TEX>$Gamma$</TEX>-ring. (3) Let M be a semi-prime <TEX>$Gamma$</TEX>-ring and <TEX>$C_{gamma}$</TEX> the extended centroid of M. If <TEX>$C_{gamma}$</TEX> is a <TEX>$Gamma$</TEX>-field, then the <TEX>$Gamma$</TEX>-ring M is a prime <TEX>$Gamma$</TEX>-ring." @default.
- W107540619 created "2016-06-24" @default.
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- W107540619 date "2004-04-01" @default.
- W107540619 modified "2023-10-16" @default.
- W107540619 title "REGULARITY OF THE GENERALIZED CENTROID OF SEMI-PRIME GAMMA RINGS" @default.
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- W107540619 doi "https://doi.org/10.4134/ckms.2004.19.2.233" @default.
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