Hilbert functions and the extension functor
1989 ◽
Vol 105
(3)
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pp. 441-446
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Throughout R will denote a commutative ring with identity, A,B etc. will denote ideals of R, and E will denote a unitary R-module. We recall from [5] the definition of homological grade hgrR(A;E) as inf{r|ExtRr(R/A,E) ≠ 0}, and we allow both hgrR(A;E) = ∞ (i.e. ExtRr(R/A,E) = 0 for all r) and AE = E. For the most part E will be Noetherian, in which case hgrR(A;E) coincides with the usual grade grR(A;E) which is the supremum of the lengths of the (weak) E-sequences contained in A (see [7], for example).
1967 ◽
Vol 63
(3)
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pp. 569-578
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1960 ◽
Vol 17
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pp. 89-110
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1997 ◽
Vol 122
(1)
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pp. 55-71
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2019 ◽
Vol 32
(2)
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pp. 103
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2016 ◽
Vol 15
(06)
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pp. 1650104
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