Equational theories and universal theories of fields

Hiroakira ONO

doi:10.2969/jmsj/03520289

Hiroakira ONO

著者情報

ジャーナルフリー

1983 年 35 巻 2 号 p. 289-306

DOI https://doi.org/10.2969/jmsj/03520289

詳細

Published: 1983 Received: 1982/01/11 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) J. Ax, Solving diophantine problems modulo every prime, Ann. of Math., 85 (1967), 161-183.
2) J. Ax, The elementary theory of finite fields, Ann. of Math., 88 (1968), 239-271.
3) C.C. Chang and H.J. Keisler, Model theory, North-Holland, Amsterdam-New York- Oxford, 1973.
4) Ju. L. Eršov, Fields with a solvable theory, Soviet Math. Dokl., 8 (1967), 575-576.
5) L. Fuchs, Partially ordered algebraic systems, Pergamon Press, New York, 1963.
6) G. Grätzer, Universal algebra, 2nd ed., Springer, New York-Heidelberg-Berlin, 1979.
7) N. Jacobson, Lectures in abstract algebra III; Theory of fields and Galois theory, D, van Nostrand, Princeton-Toronto-New York-London, 1964.
8) M. Jarden, Elementary statements over large algebraic fields, Trans. Amer. Math. Soc., 164 (1972), 67-91.
9) Y. Komori, Free algebras over all fields and pseudo-fields, Rep. Fac. Sci., Shizuoka Univ., 10 (1975), 9-15.
10) Y. Komori, A relation between strongly regular rings and pseudo-fields, Rep. Fac. Sci., Shizuoka Univ., 11 (1976), 23-24.
11) R.L. Kruse, Identities satisfied by a finite ring, J. Algebra, 26 (1973), 298-318.
12) J. Lambek, Lectures on rings and modules, Blaisdell, Waltham-Toronto-London, 1966.
13) S. Lang, Introduction to algebraic geometry, Interscience, New York, 1958.
14) S. Lang, Diophantine geometry, Interscience, New York, 1962.
15) L. Lipshitz and D. Saracino, The model companion of the theory of commutative rings without nilpotent elements, Proc. Amer. Math. Soc., 38 (1973), 381-387.
16) J. Robinson, Definability and decision problems in arithmetic, J. Symbolic Logic, 14 (1949), 98-114.
17) R.S. Rumely, Undecidability and definability for the theory of global fields, Trans. Amer. Math. Soc., 262 (1980), 195-217.
18) J.R. Shoenfield, Mathematical logic, Addison-Wesley, Reading, 1967.
19) A. Tarski, A. Mostowski and R.M. Robinson, Undecidable theories, North-Holland, Amsterdam, 1953.
20) A. Tarski, Equationally complete rings and relation algebras, Indag. Math., 18 (1956), 39-46.
21) W.H. Wheeler, Model-complete theories of pseudo-algebraically closed fields, Ann. Math. Log., 17 (1979), 205-226.

Right : [1] J. Ax, Solving diophantine problems modulo every prime, Ann. of Math., 85 (1967), 161-183.
[2] J. Ax, The elementary theory of finite fields, Ann. of Math., 88 (1968), 239-271.
[3] C. C. Chang and H. J. Keisler, Model theory, North-Holland, Amsterdam-New York- Oxford, 1973.
[4] Ju. L. Eršov, Fields with a solvable theory, Soviet Math. Dokl., 8 (1967), 575-576.
[5] L. Fuchs, Partially ordered algebraic systems, Pergamon Press, New York, 1963.
[6] G. Grätzer, Universal algebra, 2nd ed., Springer, New York-Heidelberg-Berlin, 1979.
[7] N. Jacobson, Lectures in abstract algebra III; Theory of fields and Galois theory, D. van Nostrand, Princeton-Toronto-New York-London, 1964.
[8] M. Jarden, Elementary statements over large algebraic fields, Trans. Amer. Math. Soc., 164 (1972), 67-91.
[9] Y. Komori, Free algebras over all fields and pseudo-fields, Rep. Fac. Sci., Shizuoka Univ., 10 (1975), 9-15.
[10] Y. Komori, A relation between strongly regular rings and pseudo-fields, Rep. Fac. Sci., Shizuoka Univ., 11 (1976), 23-24.
[11] R. L. Kruse, Identities satisfied by a finite ring, J. Algebra, 26 (1973), 298-318.
[12] J. Lambek, Lectures on rings and modules, Blaisdell, Waltham-Toronto-London, 1966.
[13] S. Lang, Introduction to algebraic geometry, Interscience, New York, 1958.
[14] S. Lang, Diophantine geometry, Interscience, New York, 1962.
[15] L. Lipshitz and D. Saracino, The model companion of the theory of commutative rings without nilpotent elements, Proc. Amer. Math. Soc., 38 (1973), 381-387.
[16] J. Robinson, Definability and decision problems in arithmetic, J. Symbolic Logic, 14 (1949), 98-114.
[17] R. S. Rumely, Undecidability and definability for the theory of global fields, Trans. Amer. Math. Soc., 262 (1980), 195-217.
[18] J. R. Shoenfield, Mathematical logic, Addison-Wesley, Reading, 1967.
[19] A. Tarski, A. Mostowski and R. M. Robinson, Undecidable theories, North-Holland, Amsterdam, 1953.
[20] A. Tarski, Equationally complete rings and relation algebras, Indag. Math., 18 (1956), 39-46.
[21] W. H. Wheeler, Model-complete theories of pseudo-algebraically closed fields, Ann. Math. Log., 17 (1979), 205-226.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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