Localizing prime idempotent kernel functors

Author:
S. K. Sim

Journal:
Proc. Amer. Math. Soc. **47** (1975), 335-337

MSC:
Primary 16A62

DOI:
https://doi.org/10.1090/S0002-9939-1975-0369436-7

MathSciNet review:
0369436

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Abstract: In this note, we call a prime idempotent kernel functor a localizing prime if it has the so-called property (T) of Goldman. We generalize a theorem of Heinicke to characterize localizing prime idempotent kernel functors and present an example of a prime idempotent kernel functor on , the category of unitary right -modules, which is not a localizing prime, even though is a right artinian ring.

**[1]**O. Goldman,*Rings and modules of quotients*, J. Algebra**13**(1969), 10-47. MR**39**#6914. MR**0245608 (39:6914)****[2]**A. G. Heinicke,*On the ring of quotients at a prime ideal of a right Noetherian ring*, Canad. J. Math.**24**(1972), 703-712. MR**45**#8681. MR**0299633 (45:8681)****[3]**J. Lambek and G. Michler,*The torsion theory at a prime ideal of a right Noetherian ring*, J. Algebra**25**(1973), 364-389. MR**0316487 (47:5034)****[4]**B. L. Osofsky,*A generalization of quasi-Frobenius rings*, J. Algebra**4**(1966), 373-387. MR**34**#4305. MR**0204463 (34:4305)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0369436-7

Keywords:
Idempotent kernel functor,
prime idempotent kernel functor,
property (T),
localizing prime idempotent kernel functor,
module of quotients,
ring of quotients,
supporting module,
irreducible module,
right artinian ring,
right noetherian ring,
socle

Article copyright:
© Copyright 1975
American Mathematical Society