GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES

A challenging problem in recent years has been to find a good description of the radical of a submodule N of a (Noetherian) module M over a commutative ring, where the radical of N is the intersection of all prime submodules of M which contain N. In this paper we give a description of the radical of N in a Noetherian module M which is amenable to computation either by hand in simple cases or by using a computer algebra system in other cases, and illustrate this by examples.

Tam Metin

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R. B. Ash, A course http://www.math.uiuc.edu/ r-ash/ComAlg.html, 2003. in commutative algebra, Available at
D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Springer-Verlag, New York, 1995.
D. Eisenbud, C. Huneke, and W. Vasconcelos, Direct methods for primary decomposition, Invent. Math., 110 (1992), 207-235.
L. Fuchs, W. Heinzer, and B. Olberding, Commutative ideal theory without finiteness conditions: Primal ideals, Trans. Amer. Math. Soc., 357 (2005), 2798.
J. Jenkins and P. F. Smith, On the prime radical of a module over a commu- tative ring, Comm. Algebra, 20 (1992), 3593-3602.
Kah Hin Leung and Shing Hing Man, On commutative Noetherian rings which satisfy the radical formula, Glasgow Math. J., 39 (1997), 285-293.
C.-P. Lu, Prime submodules of modules, Comm. Math. Univ. Sancti Pauli, 33 (1984), 61-69.
C.-P. Lu, M-radicals of submodules in modules II, Math. Japonica, 35 (1990), 1001.
A. Marcelo and C. Rodriguez, Radicals of submodules and symmetric algebra, Comm. Algebra, 28 (2000), 4611-4617.
R. L. McCasland, Some commutative ring results generalized to unitary mod- ules, Ph.D. thesis, University of Texas at Arlington, 1983.
R. L. McCasland and M. E. Moore, On radicals of submodules of finitely gen- erated modules, Canad. Math. Bull., 29 (1986), 37-39.
R. L. McCasland and M. E. Moore, On radicals of submodules, Comm. Algebra, (1991), 1327-1341.
R. L. McCasland and M. E. Moore, Prime submodules, Comm. Algebra, 20 (1992), 1803-1817.
R. L. McCasland, J. B. A. Schmidt, P. F. Smith, and E. M. Stark, Uniform dimension and radical modules, University of Glasgow Preprint 99/19 (1999).
R. L. McCasland and P. F. Smith, Prime submodules of Noetherian modules, Rocky Mountain J. Math., 23 (1993), 1041-1062.
R. L. McCasland and P. F. Smith, Uniform dimension of modules, Q. J. Math., (2004), 491-498.
R. L. McCasland and P. F. Smith, On isolated submodules, Comm. Algebra, (2006), 2977-2988.
P. F. Smith, Primary modules over commutative rings, Glasgow. Math. J., 43 (2001), 103-111.
Wang Fanggui and R. L. McCasland, On w-modules over strong Mori domains, Comm. Algebra, 25 (1997), 1285-1306. R.L. McCasland
School of Informatics University of Edinburgh Edinburgh EH8 9LE, Scotland UK e-mail: rmccasla@inf.ed.ac.uk P.F. Smith Department of Mathematics University of Glasgow Glasgow G12 8QW, Scotland UK e-mail: pfs@maths.gla.ac.uk

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Bibtex	@ { ieja266380, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2008}, volume = {4}, number = {4}, pages = {159 - 176}, title = {GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES}, key = {cite}, author = {Mccasland, R. L. and Smith, P. F.} }
APA	Mccasland, R. L. & Smith, P. F. (2008). GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES . International Electronic Journal of Algebra , 4 (4) , 159-176 .
MLA	Mccasland, R. L. , Smith, P. F. "GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES" . International Electronic Journal of Algebra 4 (2008 ): 159-176 <
Chicago	Mccasland, R. L. , Smith, P. F. "GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES". International Electronic Journal of Algebra 4 (2008 ): 159-176
RIS	TY - JOUR T1 - GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES AU - R. L.Mccasland, P. F.Smith Y1 - 2008 PY - 2008 N1 - DO - T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 159 EP - 176 VL - 4 IS - 4 SN - 1306-6048-1306-6048 M3 - UR - Y2 - 2022 ER -
EndNote	%0 International Electronic Journal of Algebra GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES %A R. L. Mccasland , P. F. Smith %T GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES %D 2008 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 4 %N 4 %R %U
ISNAD	Mccasland, R. L. , Smith, P. F. . "GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES". International Electronic Journal of Algebra 4 / 4 (Aralık 2008): 159-176 .
AMA	Mccasland R. L. , Smith P. F. GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES. IEJA. 2008; 4(4): 159-176.
Vancouver	Mccasland R. L. , Smith P. F. GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES. International Electronic Journal of Algebra. 2008; 4(4): 159-176.
IEEE	R. L. Mccasland ve P. F. Smith , "GENERALISED ASSOCIATED PRIMES AND RADICALS OF SUBMODULES", , c. 4, sayı. 4, ss. 159-176, Ara. 2008

International Electronic Journal of Algebra

ISSN: 1306-6048
Yayın Aralığı: Yılda Aylık
Yayıncı: Abdullah HARMANCI

24.4b99