On graded rings with finiteness conditions
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- by V. P. Camillo and K. R. Fuller PDF
- Proc. Amer. Math. Soc. 86 (1982), 1-5 Request permission
Abstract:
It is proved that a graded ring that is finitely graded modulo its radical is local if its initial subring is local, and that a graded artinian ring is finitely generated over its initial subring which is also artinian. These results extend theorems of Gordon and Green on artin algebras. Other results relating the structure of a graded ring to that of its initial subring are also presented.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 G. Bergman, On Jacobson radicals of graded rings, preprint.
- Robert Fossum and Hans-Bjørn Foxby, The category of graded modules, Math. Scand. 35 (1974), 288–300. MR 379473, DOI 10.7146/math.scand.a-11553
- Robert Gordon and Edward L. Green, Graded Artin algebras, J. Algebra 76 (1982), no. 1, 111–137. MR 659212, DOI 10.1016/0021-8693(82)90240-X —, Representation theory of graded artin algebras, preprint.
- Constantin Năstăsescu and F. Van Oystaeyen, Graded and filtered rings and modules, Lecture Notes in Mathematics, vol. 758, Springer, Berlin, 1979. MR 551625
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 1-5
- MSC: Primary 16A03; Secondary 16A10, 16A35, 16A51
- DOI: https://doi.org/10.1090/S0002-9939-1982-0663852-5
- MathSciNet review: 663852