We study the construction of new multiplication modules relative to a torsion theory $\tau $. As a consequence, $\tau $-finitely generated modules over a Dedekind domain are completely determined. We relate the relative multiplication modules to the distributive ones.
@article{118918, author = {Jos\'e Escoriza and Blas Torrecillas}, title = {Relative multiplication and distributive modules}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {38}, year = {1997}, pages = {205-221}, zbl = {0887.13002}, mrnumber = {1455487}, language = {en}, url = {http://dml.mathdoc.fr/item/118918} }
Escoriza, José; Torrecillas, Blas. Relative multiplication and distributive modules. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 205-221. http://gdmltest.u-ga.fr/item/118918/
Modules arithmétiques, Acta Math. A. S. Hung. 25 (3-4) (1974), 299-311. (1974) | MR 0357383
Multiplication modules, J. of Algebra 71 (1981), 174-178. (1981) | MR 0627431 | Zbl 0468.13011
Local cohomology and localization, Pitman Research Notes in Mathematics Series 226, Longman Scientific and Technical, Harlowe, 1989. | MR 1088249 | Zbl 0691.14003
Distributive modules, J. of Algebra 36 (1975), 16-25. (1975) | MR 0573061 | Zbl 0308.16015
Multiplication modules, Comm. in Algebra 16 (4) (1988), 755-779. (1988) | MR 0932633 | Zbl 0642.13003
Multiplication modules relative to torsion theories, Comm. in Algebra 23 (11) (1995), 4315-4331. (1995) | MR 1351136 | Zbl 0849.13008
Multiplicative ideal theory, Marcel Dekker, New York, 1972. | MR 0427289 | Zbl 0804.13001
Multiplication rings via their total quotient rings, Can. J. Math. XXVI (2) (1974), 430-449. (1974) | MR 0340238 | Zbl 0259.13007
The residual of finitely generated multiplication modules, Arch. Math. 46 (1986), 225-230. (1986) | MR 0834840 | Zbl 0573.13001
Multiplicative theory of ideals, Pure and Applied Mathematics 43 Academic Press, New York, 1979. | MR 0414528 | Zbl 0237.13002
Multiplication modules, Canad. Math. Bull. 22 (1) (1979), 93-98. (1979) | MR 0532275 | Zbl 0408.13002
La structure des modules par rapport à une topologie additive, Tôhoku Math. Journal 26 (1974), 173-201. (1974) | MR 0349765
On non-commutative AM-rings, Houston J. of Math. 11.3 (1985), 405-422. (1985) | Zbl 0608.16009
Some remarks on multiplication modules, Arch. Math. 50 (1988), 223-235. (1988) | MR 0933916 | Zbl 0615.13003
Projective ideals of finite type, Canad. J. Math. 21 (1969), 1057-1061. (1969) | MR 0246864 | Zbl 0183.04001
Rings of Quotiens, Springer-Verlag, Berlin, 1975. | MR 0389953
Modules whose lattice of submodules is distributive, Proc. London Math. Soc. 3 28 (1974), 291-310. (1974) | MR 0338082 | Zbl 0294.16003
Some properties of non-commutative multiplication rings, Proc. Japan Acad. 54 Ser. A (1978), 279-284. (1978) | MR 0517670 | Zbl 0434.16004
Left noetherian multiplication rings, Osaka J. Math. 17 (1980), 449-453. (1980) | MR 0587765 | Zbl 0444.16023
Some remarks on $M$-rings, Math. Japonica 28 2 (1983), 195-203. (1983) | MR 0699583 | Zbl 0517.16026