Joseph Becker and Leonard Lipshitz. Remarks on the elementary theories of formal and convergent power series. Fundament a mathematicae, vol. 105 (1980), pp. 229–239. - Françoise Delon. Indécidabilité de la théorie des anneaux de séries formelles à plusiers indéterminées. Fundament a mathematicae, vol. 112 (1981), pp. 215–229. - J. Becker, J. Denef, and L. Lipshitz. Further remarks on the elementary theory of formal power series rings. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 1–9. - Françoise Delon. Hensel fields in equal characteristic p > 0. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 108–116.

1985 ◽  
Vol 50 (3) ◽  
pp. 853-854
Author(s):  
S. Basarab

Angus Macintyre, Kenneth McKenna, and Lou van den Dries. Elimination of quantifiers in algebraic structures. Advances in mathematics, vol. 47 (1983), pp. 74–87. - L. P. D. van den Dries. A linearly ordered ring whose theory admits elimination of quantifiers is a real closed field. Proceedings of the American Mathematical Society, vol. 79 (1980), pp. 97–100. - Bruce I. Rose. Rings which admit elimination of quantifiers. The journal of symbolic logic, vol. 43 (1978), pp. 92–112; Corrigendum, vol. 44 (1979), pp. 109–110. - Chantal Berline. Rings which admit elimination of quantifiers. The journal of symbolic logic, vol. 43 (1978), vol. 46 (1981), pp. 56–58. - M. Boffa, A. Macintyre, and F. Point. The quantifier elimination problem for rings without nilpotent elements and for semi-simple rings. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 20–30. - Chantal Berline. Elimination of quantifiers for non semi-simple rings of characteristic p. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 10–19.

1985 ◽  
Vol 50 (4) ◽  
pp. 1079-1080
Author(s):  
Gregory L. Cherlin

2011 ◽  
Vol 31 (1) ◽  
pp. 331-343 ◽  
Author(s):  
Steven T. Dougherty ◽  
Liu Hongwei

1989 ◽  
Vol 32 (3) ◽  
pp. 314-319
Author(s):  
Peter Seibt

AbstractDifferentially simple local noetherian Q -algebras are shown to be always (a certain type of) subrings of formal power series rings. The result is established as an illustration of a general theory of differential filtrations and differential completions.


2020 ◽  
Vol 27 (03) ◽  
pp. 495-508
Author(s):  
Ahmed Maatallah ◽  
Ali Benhissi

Let A be a ring. In this paper we generalize some results introduced by Aliabad and Mohamadian. We give a relation between the z-ideals of A and those of the formal power series rings in an infinite set of indeterminates over A. Consider A[[XΛ]]3 and its subrings A[[XΛ]]1, A[[XΛ]]2, and A[[XΛ]]α, where α is an infinite cardinal number. In fact, a z-ideal of the rings defined above is of the form I + (XΛ)i, where i = 1, 2, 3 or an infinite cardinal number and I is a z-ideal of A. In addition, we prove that the same condition given by Aliabad and Mohamadian can be used to get a relation between the minimal prime ideals of the ring of the formal power series in an infinite set of indeterminates and those of the ring of coefficients. As a natural result, we get a relation between the z°-ideals of the formal power series ring in an infinite set of indeterminates and those of the ring of coefficients.


2019 ◽  
Vol 19 (01) ◽  
pp. 2050003
Author(s):  
Abolfazl Tarizadeh

In this paper, the ring of polynomials is studied in a systematic way through the theory of monoid rings. As a consequence, this study provides canonical approaches in order to find easy and rigorous proofs and methods for many facts on polynomials and formal power series; some of them as sample are treated in this paper. Besides the universal properties of the monoid rings and polynomial rings, a universal property for the formal power series rings is also established.


Sign in / Sign up

Export Citation Format

Share Document