Frobenius extensions of QF-3 rings

Kitamura, Yoshimi

doi:10.1090/S0002-9939-1980-0572295-2

Frobenius extensions of QF-$3$ rings
HTML articles powered by AMS MathViewer

by Yoshimi Kitamura PDF

Proc. Amer. Math. Soc. 79 (1980), 527-532 Request permission

Abstract:

We investigate the inheritance of QF-3 property for ring extensions, mainly, for Frobenius extensions. Let A be a ring with identity. It is proved that a group ring $A[G]$ of A with a finite group G is left QF-3 iff A is left QF-3 and that in case A is a. G-Galois extension of the fixed subring ${A^G}$ relative to a finite group G of ring automorphism of A, A is left QF-3 iff ${A^G}$ is left QF-3.

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
R. R. Colby and E. A. Rutter Jr., $\textrm {QF}-3$ rings with zero singular ideal, Pacific J. Math. 28 (1969), 303–308. MR 244318
Masatosi Ikeda and Tadasi Nakayama, On some characteristic properties of quasi-Frobenius and regular rings, Proc. Amer. Math. Soc. 5 (1954), 15–19. MR 60489, DOI 10.1090/S0002-9939-1954-0060489-9

Projective Frobenius-Erweiterungen

1960

61

Yoshimi Kitamura, On quasi-Frobenius extensions, Math. J. Okayama Univ. 15 (1971/72), 41–48. MR 301046
Kenneth Louden, Maximal quotient rings of ring extensions, Pacific J. Math. 62 (1976), no. 2, 489–496. MR 407059
Yôichi Miyashita, Finite outer Galois theory of non-commutative rings, J. Fac. Sci. Hokkaido Univ. Ser. I 19 (1966), 114–134. MR 0210752
Bruno Müller, Quasi-Frobenius-Erweiterungen, Math. Z. 85 (1964), 345–368 (German). MR 182643, DOI 10.1007/BF01110680
Takesi Onodera, Some studies on projective Frobenius extensions, J. Fac. Sci. Hokkaido Univ. Ser. I 18 (1964), 89–107. MR 0174589
Hiroyuki Tachikawa, Quasi-Frobenius rings and generalizations. $\textrm {QF}-3$ and $\textrm {QF}-1$ rings, Lecture Notes in Mathematics, Vol. 351, Springer-Verlag, Berlin-New York, 1973. Notes by Claus Michael Ringel. MR 0349740
P. Vámos, The dual of the notion of “finitely generated”, J. London Math. Soc. 43 (1968), 643–646. MR 248171, DOI 10.1112/jlms/s1-43.1.643