×

zbMATH — the first resource for mathematics

Base fields of csp-rings. (English. Russian original) Zbl 1270.13003
Algebra Logic 49, No. 4, 378-385 (2010); translation from Algebra Logika 49, No. 4, 555-565 (2010).
Summary: We study the question which fields may serve as base fields for csp-rings. It is proved that every algebraic extension of a field \(\mathbb Q\) is the base field of some csp-ring. Also it shown that in studying base fields, we may confine ourselves to treating only csp-rings of idempotent cocharacteristic, or only regular csp-rings.

MSC:
13A99 General commutative ring theory
12F99 Field extensions
13B02 Extension theory of commutative rings
Keywords:
csp-ring; base field
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] A. A. Fomin, ”Some mixed abelian groups as modules over the ring of pseudo-rational numbers,” in Abelian Groups and Modules, Birkhäuser, Basel (1999), pp. 87–100. · Zbl 0947.20037
[2] P. A. Krylov, ”Mixed Abelian groups as modules over their endomorphism rings,” Fund. Appl. Math., 6, No. 3, 793–812 (2000). · Zbl 1019.20023
[3] P. A. Krylov, ”Hereditary endomorphism rings of mixed abelian groups,” Sib. Mat. Zh., 43, No. 1, 108–119 (2002). · Zbl 1013.20052
[4] L. Fuchs and I. Halperin, ”On the imbedding of a regular ring in a regular ring with identity,” Fund. Math., 54, 285–290 (1964). · Zbl 0143.05401
[5] L. Fuchs and K. M. Rangaswamy, ”On generalized regular rings,” Math. Z., 107, No. 1, 71–81 (1968). · Zbl 0167.03401
[6] A. V. Tsarev, ”Modules over the ring of pseudorational numbers and quotient divisible groups,” Alg. Anal., 18, No. 4, 198–214 (2006). · Zbl 1137.16003
[7] A. V. Tsarev, ”Projective and generating modules over the ring of pseudorational numbers,” Mat. Zametki, 80, No. 3, 437–448 (2006). · Zbl 1137.16003
[8] E. G. Zinov’ev, ”csp-Rings as a generalization of rings of pseudo-rational numbers,” Fund. Prikl. Mat., 13, No. 3, 35–38 (2007).
[9] E. G. Zinov’ev, ”Injective and divisible modules over csp-rings,” Vestnik TGU, 299, 96–97 (2007).
[10] E. G. Zinov’ev, ”Finitely generated modules over rings of pseudoalgebraic numbers,” in Proc. Int. Alg. Conf. Dedicated to the 100th Anniversary of A. G. Kurosh, Moscow (2008), pp. 104–105.
[11] U. F. Albrecht, H. P. Goeters, and W. Wickless, ”The flat dimension of mixed Abelian groups as E-modules,” Rocky Mt. J. Math., 25, No. 2, 569–590 (1995). · Zbl 0843.20045
[12] S. B. Katok, p-Adic Analysis vs. Real-Valued Analysis [in Russian], Moscow (2004).
[13] M. C. Butler, On locally free torsion-free rings of finite rank, J. London Math. Soc., 43, No. 1 (1968), 297–300. · Zbl 0155.07202
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.