On generalized cancellation problem

Alexei Belov, Leonid Makar-Limanov, Jie Tai Yu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A well-known cancellation problem of Zariski asks whether for two given domains (fields) K1 and K2, an isomorphism of K1 [t] (K (t)) and K2 [t] (K1 (t)) implies an isomorphism of K1 and K1. In this paper, we address a related problem: whether the ring (field) embedding of K1 [t] (K1 (t)) into K2 [t] (K1 (t)) implies the ring (field) embedding of K1 into K2? Our main result is affirmative: if K1 and K2 are arbitrary domains (fields) of the finite transcendence degree and K1 [t] (K1 (t)) can be embedded into K2 [t] (K2 (t)) then K1 can be embedded into K1. As a consequence, we answer a question of Abhyankar, Eakin and Heinzer [J. Algebra 23 (1972) 310-342].

Original languageEnglish
Pages (from-to)161-166
Number of pages6
JournalJournal of Algebra
Volume281
Issue number1
DOIs
StatePublished - 1 Nov 2004
Externally publishedYes

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: [email protected], [email protected] (A. Belov), [email protected], [email protected] (L. Makar-Limanov), [email protected] (J.-T. Yu). URL: http://hkumath.hku.hk/~jtyu (J.-T. Yu). 1 Partially supported by an NSA grant. 2 Partially supported by Hong Kong RGC-CERG Grants 10203186 and 10203669.

Funding

* Corresponding author. E-mail addresses: [email protected], [email protected] (A. Belov), [email protected], [email protected] (L. Makar-Limanov), [email protected] (J.-T. Yu). URL: http://hkumath.hku.hk/~jtyu (J.-T. Yu). 1 Partially supported by an NSA grant. 2 Partially supported by Hong Kong RGC-CERG Grants 10203186 and 10203669.

FundersFunder number
National Sanitarium Association10203669, 10203186

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