Testing Equality in Differential Ring Extensions Defined by PDE's and Limit Conditions

2002 ◽  
Vol 13 (4) ◽  
pp. 257-288 ◽  
Author(s):  
Ariane Péladan-Germa
Keyword(s):  
Differential Ring ◽  
Ring Extensions

Extensions of Rings Having McCoy Condition

2009 ◽  
Vol 52 (2) ◽  
pp. 267-272 ◽  
Author(s):  
Muhammet Tamer Koşan
Keyword(s):  
Positive Integer ◽  
Associative Ring ◽  
Nonzero Element ◽  
Ring Extensions

AbstractLet R be an associative ring with unity. Then R is said to be a right McCoy ring when the equation f (x)g(x) = 0 (over R[x]), where 0 ≠ f (x), g(x) ∈ R[x], implies that there exists a nonzero element c ∈ R such that f (x)c = 0. In this paper, we characterize some basic ring extensions of right McCoy rings and we prove that if R is a right McCoy ring, then R[x]/(xn) is a right McCoy ring for any positive integer n ≥ 2.

scholarly journals Injective modules under faithfully flat ring extensions

2015 ◽  
Vol 144 (3) ◽  
pp. 1015-1020 ◽  
Author(s):  
Lars Winther Christensen ◽  
Fatih Köksal
Keyword(s):  
Injective Modules ◽  
Flat Ring ◽  
Ring Extensions

A low power consumption CMOS differential-ring VCO for a wireless sensor

2012 ◽  
Vol 73 (3) ◽  
pp. 731-740 ◽  
Author(s):  
Hanen Thabet ◽  
Stéphane Meillère ◽  
Mohamed Masmoudi ◽  
Jean-Luc Seguin ◽  
Hervé Barthelemy ◽  
...  
Keyword(s):  
Power Consumption ◽  
Low Power ◽  
Wireless Sensor ◽  
Low Power Consumption ◽  
Differential Ring

On Radicals of Skew Inverse Laurent Series Rings

2016 ◽  
Vol 23 (02) ◽  
pp. 335-346
Author(s):  
A. Moussavi
Keyword(s):  
Polynomial Ring ◽  
Jacobson Radical ◽  
Laurent Series ◽  
Ring Extensions ◽  
Series Type ◽  
Armendariz Ring

Let R be a ring and α an automorphism of R. Amitsur proved that the Jacobson radical J(R[x]) of the polynomial ring R[x] is the polynomial ring over the nil ideal J(R[x]) ∩ R. Following Amitsur, it is shown that when R is an Armendariz ring of skew inverse Laurent series type and S is any one of the ring extensions R[x;α], R[x,x-1;α], R[[x-1;α]] and R((x-1;α)), then ℜ𝔞𝔡(S) = ℜ𝔞𝔡(R)S = Nil (S), ℜ𝔞𝔡(S) ∩ R = Nil (R), where ℜ𝔞𝔡 is a radical in a class of radicals which includes the Wedderburn, lower nil, Levitzky and upper nil radicals.

Analysis of frequency and amplitude in CMOS differential ring oscillators

Integration ◽  
2016 ◽  
Vol 52 ◽  
pp. 253-259 ◽  
Author(s):  
Hojat Ghonoodi ◽  
Hossein Miar-Naimi ◽  
Mohammad Gholami
Keyword(s):  
Ring Oscillators ◽  
Differential Ring

Commutative rings and modules that are Nil*-coherent or special Nil*-coherent

2017 ◽  
Vol 16 (10) ◽  
pp. 1750187 ◽  
Author(s):  
Karima Alaoui Ismaili ◽  
David E. Dobbs ◽  
Najib Mahdou
Keyword(s):  
Commutative Rings ◽  
Finitely Generated ◽  
Basic Properties ◽  
Unital Ring ◽  
Reduced Ring ◽  
Coherent Ring ◽  
Ring Extensions ◽  
Coherent Rings ◽  
Finitely Presented

Recently, Xiang and Ouyang defined a (commutative unital) ring [Formula: see text] to be Nil[Formula: see text]-coherent if each finitely generated ideal of [Formula: see text] that is contained in Nil[Formula: see text] is a finitely presented [Formula: see text]-module. We define and study Nil[Formula: see text]-coherent modules and special Nil[Formula: see text]-coherent modules over any ring. These properties are characterized and their basic properties are established. Any coherent ring is a special Nil[Formula: see text]-coherent ring and any special Nil[Formula: see text]-coherent ring is a Nil[Formula: see text]-coherent ring, but neither of these statements has a valid converse. Any reduced ring is a special Nil[Formula: see text]-coherent ring (regardless of whether it is coherent). Several examples of Nil[Formula: see text]-coherent rings that are not special Nil[Formula: see text]-coherent rings are obtained as byproducts of our study of the transfer of the Nil[Formula: see text]-coherent and the special Nil[Formula: see text]-coherent properties to trivial ring extensions and amalgamated algebras.

On the Generalized Auslander–Reiten Conjecture under Certain Ring Extensions

2015 ◽  
Vol 58 (1) ◽  
pp. 134-143
Author(s):  
Saeed Nasseh
Keyword(s):  
Local Ring ◽  
Gorenstein Ring ◽  
Ring Extensions

AbstractWe show that under some conditions a Gorenstein ring R satisfies the Generalized Auslander–Reiten conjecture if and only if R[x] does. When R is a local ring we prove the same result for some localizations of R[x].

AB-5* for Module and Ring Extensions

2019 ◽  
pp. 59-68 ◽  
Author(s):  
Pham Ngoc Ánh ◽  
Dolors Herbera ◽  
Claudia Menini
Keyword(s):  
Ring Extensions

scholarly journals Maximal quotient rings of ring extensions

1976 ◽  
Vol 62 (2) ◽  
pp. 489-496 ◽  
Author(s):  
Kenneth Louden
Keyword(s):  
Ring Extensions ◽  
Quotient Rings

scholarly journals Generalized fractional differential ring

2021 ◽  
Vol 5 (1) ◽  
pp. 279-287
Author(s):  
Zeinab Toghani ◽  
◽  
Luis Gaggero-Sager ◽  
Keyword(s):  
Fractional Derivative ◽  
Infinite Number ◽  
Fractional Derivatives ◽  
Differential Operators ◽  
Differential Ring ◽  
Fractional Differential

There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there is an infinite number of possible definitions of fractional derivatives, all are correct as differential operators each of them must be properly defined its algebra. We introduce a generalized version of fractional derivative that extends the existing ones in the literature. To those extensions it is associated a differentiable operator and a differential ring and applications that shows the advantages of the generalization. We also review the different definitions of fractional derivatives and it is shown how the generalized version contains the previous ones as a particular cases.

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