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• W2024165941 startingPage "515" @default.
• W2024165941 abstract "Let R be a commutative ring with identity. Then we prove <TEX>$M_n(R)=GL_n(R)$</TEX> <TEX>${cup}$</TEX>{<TEX>$A{in}M_n(R);{mid};detA{neq}0$</TEX> and det <TEX>$A{neq}U(R)$</TEX>}<TEX>${cup}Z(M-n(R))$</TEX> where U(R) denotes the set of all units of R. In particular, it will be proved that the full matrix ring <TEX>$M_n(F)$</TEX> over a field F is the disjoint union of the general linear group <TEX>$GL_n(F)$</TEX> of degree n over the field F and the set <TEX>$Z(M_n(F))$</TEX> of all zero-divisors of <TEX>$M_n(F)$</TEX>. Using the result and universal mapping property we prove that <TEX>$M_n(F)$</TEX> is its total ring of fractions." @default.
• W2024165941 created "2016-06-24" @default.
• W2024165941 creator A5035019823 @default.
• W2024165941 date "2009-12-25" @default.
• W2024165941 modified "2023-09-24" @default.
• W2024165941 title "MATRIX RINGS AND ITS TOTAL RINGS OF FRACTIONS" @default.
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• W2024165941 doi "https://doi.org/10.5831/hmj.2009.31.4.515" @default.
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