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 language | English |
---|---|
Pages (from-to) | 161-166 |
Number of pages | 6 |
Journal | Journal of Algebra |
Volume | 281 |
Issue number | 1 |
DOIs | |
State | Published - 1 Nov 2004 |
Externally published | Yes |
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.
Funders | Funder number |
---|---|
National Sanitarium Association | 10203669, 10203186 |