The middle annihilator conjecture for embeddable rings

Author:
C. Dean

Journal:
Proc. Amer. Math. Soc. **103** (1988), 46-48

MSC:
Primary 16A34

DOI:
https://doi.org/10.1090/S0002-9939-1988-0938642-1

MathSciNet review:
938642

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that any ring which can be embedded in an Artinian ring has just finitely many middle annihilator primes. In particular, this proves the middle annihilator conjecture for a large class of Noetherian rings.

**[1]**W. D. Blair and L. W. Small,*Embeddings in Artinian rings and Sylvester rank functions*, Israel J. Math.**58**(1987), 10-18. MR**889970 (88i:16016)****[2]**A. W. Chatters and C. R. Hajarnavis,*Rings with chain conditions*, Research Notes in Math., vol. 44, Pitman, London, 1980. MR**590045 (82k:16020)****[3]**C. Dean and J. T. Stafford,*A nonembeddable Noetherian ring*, J. Algebra (in press).**[4]**A. W. Goldie and G. Krause,*Strongly regular elements of Noetherian rings*, J. Algebra**91**(1984), 410-429. MR**769583 (86d:16003)****[5]**K. R. Goodearl and R. B. Warfield, Jr., in preparation.**[6]**R. Gordon,*Primary decomposition in right Noetherian rings*, Comm. Algebra**2**(1974), 491-524. MR**0360691 (50:13138)****[7]**A. V. Jategaonkar,*Solvable Lie algebras, polycyclic-by-finite groups and bimodule Krull dimension*, Comm. Algebra**10**(1982), 19-70. MR**674687 (84i:16014)****[8]**G. Krause,*Middle annihilators in Noetherian rings*, Comm. Algebra**8**(1980), 781-791. MR**566421 (81h:16025)****[9]**A. H. Schofield,*Representations of rings over skew fields*, London Math. Soc. Lecture Note Ser., vol. 92, Cambridge Univ. Press, London and New York, 1985. MR**800853 (87c:16001)****[10]**L. W. Small,*Rings satisfying a polynomial identity*, Lecture notes, Essen, 1980. MR**601386 (82j:16028)****[11]**L. W. Small and J. T. Stafford,*Regularity of zero divisors*, Proc. London Math. Soc. (3)**44**(1982), 405-419. MR**656243 (84b:16014)****[12]**R. B. Warfield, Jr.,*Prime ideals in ring extensions*, J. London Math. Soc. (2)**28**(1983), 453-460. MR**724714 (85e:16006)**

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0938642-1

Article copyright:
© Copyright 1988
American Mathematical Society