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Article

Tiraṣ, Yücel ; Harmanci, Abdullah
On prime submodules and primary decomposition. (English). Czechoslovak Mathematical Journal, vol. 50 (2000), issue 1, pp. 83-90
MSC: 13A15, 13C05, 13C13, 13C99, 13F10 | MR 1745462 | Zbl 1036.13010
Keywords:
Prime submodule; primary submodule; primary decomposition; Associated primes
Summary:
We characterize prime submodules of $R\times R$ for a principal ideal domain $R$ and investigate the primary decomposition of any submodule into primary submodules of $R\times R.$
References:
[1] J. Jenkins and P. F. Smith: On the prime radical of a module over a commutative ring. Comm. Algebra 20 (12) (1992), 3593–3602. DOI 10.1080/00927879208824530 | MR 1191968
[2] C. P. Lu: Prime submodules of modules. Comm. Math. Univ. Sancti. Pauli 33 (1984), 61–69. MR 0741378 | Zbl 0575.13005
[3] C. P. Lu: $M$-radicals of submodules in modules. Math. Japon. 34 (1989), no. 2, 211–219. MR 0994584 | Zbl 0706.13002
[4] C. P. Lu: $M$-radicals of submodules in modules II. Math. Japon. 35 (1990), no. 5, 991–1001. MR 1073902 | Zbl 0719.13001
[5] S. M. George, R. Y. McCasland and P. F. Smith: A principal ideal theorem analogue for modules over commutative rings. Comm. Algebra 22 (6) (1994), 2083–2099. DOI 10.1080/00927879408824957 | MR 1268545
[6] R. Y. McCasland and M. E. Moore: On radicals of submodules of finitely generated modules. Canad. Math. Bull. 29 (1) (1986). DOI 10.4153/CMB-1986-006-7 | MR 0824879
[7] R. Y. McCasland and P. F. Smith: Prime submodules of Noetherian modules. Rocky Mountain J. Math. 23 (1993), no. 3. DOI 10.1216/rmjm/1181072540 | MR 1245463
[8] H. Matsumura: Commutative Ring Theory. Cambridge University Press, 1980. MR 0879273
[9] R. Y. Sharp: Steps in Commutative Algebra. Cambridge University Press, 1990. MR 1070568 | Zbl 0703.13001
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