论文信息 - Decidability of the theory of modules over commutative valuation domains

Decidability of the theory of modules over commutative valuation domains

Abstract We prove that, if V is an effectively given commutative valuation domain such that its value group is dense and archimedean, then the theory of all V -modules is decidable.

Carlo Toffalori | Gennadi Puninski | Vera Puninskaya

[1] A. Facchini. Relative injectivity and pure-injective modules over Prüfer rings , 1987 .

[2] L. Fuchs. Modules over valuation domains , 1985 .

[3] Paul C. Eklof,et al. The elementary theory of abelian groups , 1972 .

[4] Wanda Szmielew. Elementary properties of Abelian groups , 1955 .

[5] Gennadi Puninski,et al. Cantor-Bendixson Rank of the Ziegler Spectrum Over a Commutative Valuation Domain , 1999, Journal of Symbolic Logic.

[6] M. Prest. Model theory and modules , 1988 .

[7] Martin Ziegler,et al. Model theory of modules , 1984, Ann. Pure Appl. Log..

[8] D. Eisenbud,et al. Serial Rings , 1971 .