Endomorphism rings of finitely generated projective modules

Miller, Robert W.

doi:10.2140/pjm.1973.47.199

Cited by 10 publications

(5 citation statements)

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“…By our above argument (3) will follow from (1) or (2) if we can show that the flat module (A/A t ) A is protective. In (1) this follows since (A/A t ) A has a projective cover [8,Lemma 1.2]. In (2) this follows by [3, corollary to Proposition 2.2].…”

Section: ) ^ Is Closed Under Homomorphic Images and (A/a T ) A Has Amentioning

confidence: 93%

TTF classes and quasi-generators

Miller¹

1974

Pacific J. Math.

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Section: ) ^ Is Closed Under Homomorphic Images and (A/a T ) A Has Amentioning

confidence: 93%

TTF classes and quasi-generators

Miller¹

1974

Pacific J. Math.

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“…Definition 1.3 (Injector and flator). We call S P R an injector (projector, flator) in case F P = P R ⊗ − preserves injective (projective, flat) modules where S = End(P R ), that is, F P (M ) is S-injective (projective, flat) whenever M is Rinjective (projective, flat) (see [1] and [10]).…”

Section: Preliminariesmentioning

confidence: 99%

Gorenstein-Injectors, Gorenstein-Flators

Gu¹,

Zhu²,

Zhou³

2010

Journal of the Korean Mathematical Society

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Over a ring R, let P R be a finitely generated projective right R-module. Then we define the G-injector (G-projector) if P R preservers Gorenstein injective modules (Gorenstein projective modules), the Gflator if P R preservers Gorenstein flat modules. G-injector (G-flator) and G-injector are characterized focus primarily on the cases where R is a Gorenstein ring, and under this condition we also study the relations between the injector (projector, flator) and the G-injector (G-projector, G-flator). Over any ring we also give the characteristics of G-injector (Gflator) by the Gorenstein injective (Gorenstein flat) dimensions of modules.

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“…In Miller [12] defined a flatjector to be a finitely generated projective P Λ such that is flat over S for each flat B M. Dually, DEFINITION Proof. Since, over an FC ring coflats and flats are the same, it will suffice to prove the final assertion.…”

Section: S = End (P B )mentioning

confidence: 99%

“…Assume (b). Miller [12,Theorem 2.3] proved that P R and R P* are flatjectors if and only if P/ and S P are flat. By 3.2, S is an FC ring.…”

Section: S = End (P B )mentioning

confidence: 99%