On prime submodules and primary decomposition
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 1, pp. 83-90 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $R\times R.$
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 $R\times R.$
Classification : 13A15, 13C05, 13C13, 13C99, 13F10
Keywords: Prime submodule; primary submodule; primary decomposition; Associated primes
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Tiraṣ, Yücel; Harmanci, Abdullah. On prime submodules and primary decomposition. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 1, pp. 83-90. http://geodesic.mathdoc.fr/item/CMJ_2000_50_1_a10/

[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 | MR

[2] C. P. Lu: Prime submodules of modules. Comm. Math. Univ. Sancti. Pauli 33 (1984), 61–69. | MR | Zbl

[3] C. P. Lu: $M$-radicals of submodules in modules. Math. Japon. 34 (1989), no. 2, 211–219. | MR | Zbl

[4] C. P. Lu: $M$-radicals of submodules in modules II. Math. Japon. 35 (1990), no. 5, 991–1001. | MR | Zbl

[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 | MR

[6] R. Y. McCasland and M. E. Moore: On radicals of submodules of finitely generated modules. Canad. Math. Bull. 29 (1) (1986). | DOI | MR

[7] R. Y. McCasland and P. F. Smith: Prime submodules of Noetherian modules. Rocky Mountain J. Math. 23 (1993), no. 3. | DOI | MR

[8] H. Matsumura: Commutative Ring Theory. Cambridge University Press, 1980. | MR

[9] R. Y. Sharp: Steps in Commutative Algebra. Cambridge University Press, 1990. | MR | Zbl