On quotient rings of trivial extensions

Kitamura, Yoshimi

doi:10.1090/S0002-9939-1983-0699400-4

On quotient rings of trivial extensions
HTML articles powered by AMS MathViewer

by Yoshimi Kitamura PDF

Proc. Amer. Math. Soc. 88 (1983), 391-396 Request permission

Abstract:

Let $R$ be a ring with identity and $M$ a two-sided $R$-module. It is shown that every right quotient ring in the sense of Gabriel of the trivial extension of $R$ by $M$ is a trivial extension of a right quotient ring of $R$ by a suitable two-sided module in case $_RM$ is flat and finitely generated by elements which centralize with every element of $R$.

References

Frank W. Anderson and Kent R. Fuller, Rings and categories of modules, Graduate Texts in Mathematics, Vol. 13, Springer-Verlag, New York-Heidelberg, 1974. MR 0417223
Pierre Gabriel, Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323–448 (French). MR 232821
V. K. Harčenko, Galois extensions, and rings of quotients, Algebra i Logika 13 (1974), no. 4, 460–484, 488 (Russian). MR 0396636
Joachim Lambek, On Utumi’s ring of quotients, Canadian J. Math. 15 (1963), 363–370. MR 147509, DOI 10.4153/CJM-1963-041-4
Kiiti Morita, Localizations in categories of modules. I, Math. Z. 114 (1970), 121–144. MR 263858, DOI 10.1007/BF01110321
Bruno J. Müller, On Morita duality, Canadian J. Math. 21 (1969), 1338–1347. MR 255597, DOI 10.4153/CJM-1969-147-7
Yuzo Utumi, On quotient rings, Osaka Math. J. 8 (1956), 1–18. MR 78966