scholarly journals Chain of prime ideals in formal power series rings

1983 ◽  
Vol 88 (4) ◽  
pp. 591-591 ◽  
Author(s):  
Ada Maria de S. Doering ◽  
Yves Lequain
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Prime Ideals ◽  
Power Series Rings ◽  
Formal Power

A Note on z-Ideals and z°-Ideals of the Formal Power Series Rings and Polynomial Rings in an Infinite Set of Indeterminates

2020 ◽  
Vol 27 (03) ◽  
pp. 495-508
Author(s):  
Ahmed Maatallah ◽  
Ali Benhissi
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Cardinal Number ◽  
Prime Ideals ◽  
Infinite Cardinal ◽  
Series Ring ◽  
Formal Power Series Ring ◽  
Power Series Rings ◽  
Formal Power ◽  
Infinite Set

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.

Cyclic codes over formal power series rings

2011 ◽  
Vol 31 (1) ◽  
pp. 331-343 ◽  
Author(s):  
Steven T. Dougherty ◽  
Liu Hongwei
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Cyclic Codes ◽  
Power Series Rings ◽  
Formal Power

Differential Completions and Differentially Simple Algebras

1989 ◽  
Vol 32 (3) ◽  
pp. 314-319
Author(s):  
Peter Seibt
Keyword(s):  
General Theory ◽  
Power Series ◽  
Formal Power Series ◽  
Power Series Rings ◽  
Simple Algebras ◽  
Formal Power

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.

scholarly journals A fresh look into monoid rings and formal power series rings

2019 ◽  
Vol 19 (01) ◽  
pp. 2050003
Author(s):  
Abolfazl Tarizadeh
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Universal Property ◽  
Polynomial Rings ◽  
Power Series Rings ◽  
Universal Properties ◽  
Ring Of Polynomials ◽  
Formal Power

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.

scholarly journals On the content of polynomials over semirings and its applications

2016 ◽  
Vol 15 (05) ◽  
pp. 1650088 ◽  
Author(s):  
Peyman Nasehpour
Keyword(s):  
Power Series ◽  
Prime Ideal ◽  
Formal Power Series ◽  
Finite Union ◽  
Distributive Lattices ◽  
Prime Ideals ◽  
Zero Divisors ◽  
Formal Power

In this paper, we prove that Dedekind–Mertens lemma holds only for those semimodules whose subsemimodules are subtractive. We introduce Gaussian semirings and prove that bounded distributive lattices are Gaussian semirings. Then we introduce weak Gaussian semirings and prove that a semiring is weak Gaussian if and only if each prime ideal of this semiring is subtractive. We also define content semialgebras as a generalization of polynomial semirings and content algebras and show that in content extensions for semirings, minimal primes extend to minimal primes and discuss zero-divisors of a content semialgebra over a semiring who has Property ([Formula: see text]) or whose set of zero-divisors is a finite union of prime ideals. We also discuss formal power series semirings and show that under suitable conditions, they are good examples of weak content semialgebras.

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