Abstract
Prime submodules of a module N and its symmetric algebra S(N) are used to study radicals of submodules and minimal components of symmetric algebras by translating results from one categorie to the another one and vice versa.
The commutative algebra investigation group of the University of Las Palmas de Gran Canaria is enormously grateful to Jaime Muñoz Masqué for being our advisor and true friend for all past years. Above all, Jaime deserves special mention for being a nice person always willing to share his expertise in several fields of mathematics. Thanks Jaime for your extraordinary generosity and talent in writing and teaching mathematics. We are pleased to take this opportunity to express our sincere thanks.
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References
Huneke, C., Rossi, M.: The dimension and components of symmetric algebras. J. Algebra 98, 200–210 (1986)
Jenkins, J., Smith, P.F.: On the prime radical of a module over a commutative ring. Commun. Algebra 20(12), 3593–3602 (1992)
Chin-Pi, Lu: \(M\)-radicals of submodules in modules. Math. Japonica 34(2), 21–219 (1989)
Marcelo, A., Muñoz, J.: Masqué, prime submodules, the descent invariant, and modules of finite length. J. Algebra 189, 273–293 (1997)
Marcelo, A., Rodríguez, C.: Radicals of submodules and symmetric algebra. Commun. Algebra 28(10), 4611–4617 (2000)
Marcelo, A., Marcelo, F., Rodríguez, C.: Equidimensional symmetric algebras. J. Korean Math. Soc. 47(2), 289–297 (2010)
Matsumura, H.: Commutative Ring Theory. Cambridge University Press, Cambridge (1986)
McCasland, R., Moore, M.: On radicals of submodules of finitely generated modules. Can. Math. Bull. 29(1), 37–39 (1986)
McCasland, R., Moore, M.: On radicals of submodules. Commun. Algebra 19(5), 1327–1341 (1991)
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Marcelo, A., Marcelo, F., Rodríguez, C. (2016). Prime Submodules and Symmetric Algebras. In: Castrillón López, M., Hernández Encinas, L., Martínez Gadea, P., Rosado María, M. (eds) Geometry, Algebra and Applications: From Mechanics to Cryptography. Springer Proceedings in Mathematics & Statistics, vol 161. Springer, Cham. https://doi.org/10.1007/978-3-319-32085-4_13
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DOI: https://doi.org/10.1007/978-3-319-32085-4_13
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