Frobenius Full Matrix Algebras and Gorenstein Tiled Orders |
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Authors: | Hisaaki Fujita Yosuke Sakai |
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Affiliation: | 1. Institute of Mathematics, University of Tsukuba , Tsukuba, Ibaraki, Japan fujita@math.tsukuba.ac.jp;3. Institute of Mathematics, University of Tsukuba , Tsukuba, Ibaraki, Japan |
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Abstract: | It is well-known that if R is a left Noetherian ring, then there is a bijective correspondence between minimal prime ideals of R and maximal torsion radicals of R-Mod. Using the notion of a prime M-ideal, it is shown that this correspondence can be extended to the category σ[M] of modules subgenerated by a module M, provided that M is a Noetherian quasi-projective generator in σ[M]. Furthermore, under this hypothesis the prime M-ideals are the fully invariant submodules P of M such that M/P is semi-compressible. |
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Keywords: | Forbenius algebra Gorenstein tiled orders Nakayama permutation |
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