Abstract
The author studies the Green correspondence and quasi-Green correspondence for indecomposable modules over strongly graded rings. The motivation is to investigate the influence of induction and restriction processes on indecomposability of graded modules.
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Burry, D. W., A strengthened theory of vertices and sources, J. Algebra, 59(2), 1979, 330–344.
Curtis, C. W. and Reiner, I., Methods of Representation Theory, Vol. I, John Wiley, New York, 1981.
Dade, E. C., Group-graded rings and modules, Math. Z., 174(3), 1980, 241–262.
Green, J. A., On the indecomposable representations of a finite group, Math. Z., 70(1), 1958, 430–445.
Green, J. A., A transfer theorem for modular representations, J. Algebra, 1(1), 1964, 73–84.
Héthelyi, L., Szöke, M. and Lux, K., The restriction of indecomposable modules for group algebras and the quasi-Green correspondence, Comm. Algebra, 26(1), 1998, 83–95.
Héthelyi, L. and Szöke, M., Green correspondence and its generalizations, Comm. Algebra, 28(9), 2000, 4463–4479.
Hussein, S. S., Induced and restricted modules over graded rings, Proc. Math. Phys. Soc. Egypt, 76, 2001, 1–13.
Hussein, S. S., Vertices and sources of indecomposable graded modules, J. Egyptian Math. Soc., to appear.
Landrock, P. and Michler, G. O., Block structure of the smallest Janko group, Math. Ann., 232(3), 1978, 205–238.
Năstăsescu, C. and van Oystaeyen, F., Graded Ring Theory, Mathematical Library, 28, North-Holand, Amsterdam, 1982.
Năstăsescu, C. and van Oystaeyen, F., Dimensions of Ring Theory, D. Reidel Publ. Co., Boston, 1987.
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Hussein, S.ED.S. Generalized Green correspondence of graded modules. Chin. Ann. Math. Ser. B 30, 413–420 (2009). https://doi.org/10.1007/s11401-008-0347-8
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DOI: https://doi.org/10.1007/s11401-008-0347-8