$G$-codes over formal power series rings and finite chain rings

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.

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Automorphisms of formal power series rings over a valuation ring

Valuation Theory and Its Applications, Volume II ◽

10.1090/fic/033/07 ◽

2003 ◽

pp. 79-87 ◽

Cited By ~ 2

Author(s):

Barry Green

Keyword(s):

Power Series ◽

Formal Power Series ◽

Valuation Ring ◽

Power Series Rings ◽

Formal Power

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

Algebra Colloquium ◽

10.1142/s1005386720000413 ◽

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.

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A fresh look into monoid rings and formal power series rings

Journal of Algebra and Its Applications ◽

10.1142/s0219498820500036 ◽

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.

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