Some Equivalences and Dualities via Static Modules
ABSTRACT
For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and dualities between subcategories of B-modules which are finitely cogenerated injective as A-modules and E-modules and F-modules which are finitely generated projective as D-modules.
For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and dualities between subcategories of B-modules which are finitely cogenerated injective as A-modules and E-modules and F-modules which are finitely generated projective as D-modules.
KEYWORDS
Static Modules, Finitely Cogenerated Injective Modules, Finitely Generated Projective Modules
Static Modules, Finitely Cogenerated Injective Modules, Finitely Generated Projective Modules
Cite this paper
nullS. Al-Nofayee and S. Nauman, "Some Equivalences and Dualities via Static Modules," Advances in Pure Mathematics, Vol. 1 No. 6, 2011, pp. 359-362. doi: 10.4236/apm.2011.16064.
nullS. Al-Nofayee and S. Nauman, "Some Equivalences and Dualities via Static Modules," Advances in Pure Mathematics, Vol. 1 No. 6, 2011, pp. 359-362. doi: 10.4236/apm.2011.16064.
References
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[1] S. Al-Nofayee, S. K. Nauman, “Equivalences and Dualities between FCI and FGP Modules,” International Journal of Algebra, Vol. 3, No. 19, 2009, pp. 911-918. [2] W. Xue, “Characterizations of Injective Cogenerators and Morita Duality via Equivalences and Dualities,” Journal of Pure & Applied Algebra, Vol. 102, No. 1, 1995, pp. 103-107. doi:10.1016/0022-4049(95)00078-B [3] S. K. Nauman, “Static Modules and Stable Clifford Theory,” Journal of Algebra, Vol. 128, No. 2, 1990, pp. 497-509. doi:10.1016/0021-8693(90)90037-O [4] E. Cline, “Stable Clifford Theory,” Journal of Algebra, Vol. 22, No. 2, 1972, pp. 350-364. doi:10.1016/0021-8693(72)90152-4 [5] E. C. Dade, “Group-Graded Rings and Modules,” Mathe- matische Zeitschrift, Vol. 174, No. 3, 1980, pp. 241-262 doi:10.1007/BF01161413 [6] K. R. Fuller, “Ring Extensions and Duality,” Algebra and Its Applications, Contemporary Mathematics, Vol. 259, American Mathematical Society, 2000, pp. 213-222.