Chains of prime ideals in power series rings

2021 ◽  
pp. 106726
Author(s):  
Phan Thanh Toan ◽  
Byung Gyun Kang
Keyword(s):  
Power Series ◽  
Prime Ideals ◽  
Power Series Rings

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.

scholarly journals Goldie twisted partial skew power series rings

2019 ◽  
Vol 18 (08) ◽  
pp. 1950151 ◽  
Author(s):  
Wagner Cortes ◽  
Simone Ruiz
Keyword(s):  
Power Series ◽  
Laurent Series ◽  
Prime Radical ◽  
Prime Ideals ◽  
Partial Action ◽  
Unital Ring ◽  
Power Series Rings

In this paper, we work with a unital twisted partial action of [Formula: see text] on a unital ring [Formula: see text]. We introduce the twisted partial skew power series rings and twisted partial skew Laurent series rings. We study primality, semi-primality and the prime ideals in these rings. We describe the prime radical in twisted partial skew Laurent series rings. We investigate the Goldie property in twisted partial skew power series rings and twisted partial skew Laurent series rings. Moreover, we describe conditions for the semiprimality in twisted partial skew power series rings.

scholarly journals Prime Ideals of q-Commutative Power Series Rings

2010 ◽  
Vol 14 (6) ◽  
pp. 1003-1023 ◽  
Author(s):  
Edward S. Letzter ◽  
Linhong Wang
Keyword(s):  
Power Series ◽  
Prime Ideals ◽  
Power Series Rings

Prime Ideals in Birational Extensions of Two-Dimensional Power Series Rings

2013 ◽  
Vol 41 (2) ◽  
pp. 703-735 ◽  
Author(s):  
Christina Eubanks-Turner ◽  
Melissa Luckas ◽  
A. Serpil Saydam
Keyword(s):  
Power Series ◽  
Prime Ideals ◽  
Two Dimensional ◽  
Power Series Rings

Power Series Rings Over Prüfer v-multiplication Domains. II

2017 ◽  
Vol 60 (1) ◽  
pp. 63-76
Author(s):  
Gyu Whan Chang
Keyword(s):  
Power Series ◽  
Prime Ideals ◽  
Power Series Ring ◽  
Series Ring ◽  
Krull Domain ◽  
Valuation Domains ◽  
Power Series Rings ◽  
Complete Integral Closure ◽  
Minimal Prime ◽  
Type Power

AbstractLet D be an integral domain, X1(D) be the set of height-one prime ideals of D, {Xβ} and {Xα} be two disjoint nonempty sets of indeterminates over D, D[{Xβ}] be the polynomial ring over D, and D[{Xβ}][[{Xα}]]1 be the first type power series ring over D[{Xβ}]. Assume that D is a Prüfer v-multiplication domain (PvMD) in which each proper integral t-ideal has only finitely many minimal prime ideals (e.g., t-SFT PvMDs, valuation domains, rings of Krull type). Among other things, we show that if X1(D) = Ø or DP is a DVR for all P ∊ X1(D), then D[{Xβ}][[{Xα}]]1D−{0} is a Krull domain. We also prove that if D is a t-SFT PvMD, then the complete integral closure of D is a Krull domain and ht(M[{Xβ}][[{Xα}]]1) = 1 for every height-one maximal t-ideal M of D.

Prime Ideals in Polynomial and Power Series Rings over Noetherian Domains

2014 ◽  
pp. 55-82 ◽  
Author(s):  
Ela Celikbas ◽  
Christina Eubanks-Turner ◽  
Sylvia Wiegand
Keyword(s):  
Power Series ◽  
Prime Ideals ◽  
Power Series Rings
Sign in / Sign up

Export Citation Format

Share Document