Abstract
We study finite-rank torsion-free abelian groups and quotient divisible mixed groups. We consider the pseudorational rank, a new invariant for finite-rank torsion-free groups which was introduced by A. A. Fomin, and establish its connection with the usual rank. We find a condition for existence of a homomorphism from one quotient divisible group into the other.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Fuchs L., Infinite Abelian Groups. Vol. 1 and 2, Academic Press (1970, 1973).
Fomin A. A., “Some mixed abelian groups as modules over the ring of pseudo-rational numbers,” in: Proc. Dublin’s Conf. on Abelian Groups, Dublin, 1999, pp. 87–100.
P. A. Krylov (2000) ArticleTitleMixed abelian groups as modules over their endomorphism rings Fund. Prikl. Mat. 6 IssueID3 793–812
A. Fomin W. Wickless (1998) ArticleTitleQuotient divisible abelian groups Proc. Amer. Math. Soc. 126 IssueID1 45–52
A. V. Tsarev (2000) Finitely generated R-modules Nauchn. Tr. Mat. Fak. MPGU Moscow 285–289
A. A. Fomin (2001) ArticleTitleQuotient divisible mixed groups Contempt. Math. 273 117–128
A. V. Tsarev (2002) ArticleTitleA module of pseudorational relations of a group Chebyshevsk. Sb. 3 IssueID1 120–134
Author information
Authors and Affiliations
Additional information
Original Russian Text Copyright © 2005 Tsarev A. V.
Translated from Sibirski \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Matematicheski \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Zhurnal, Vol. 46, No. 1, pp. 217–229, January–February, 2005.
Rights and permissions
About this article
Cite this article
Tsarev, A.V. The pseudorational rank of an abelian group. Sib Math J 46, 172–181 (2005). https://doi.org/10.1007/s11202-005-0018-x
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11202-005-0018-x