dedekind ring
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2021 ◽  
Vol 58 (3) ◽  
pp. 367-370
Author(s):  
Abdulaziz Deajim ◽  
Lhoussain El Fadil
Keyword(s):  

In this note, we show that the result [1, Proposition 5.2] is inaccurate. We further give and prove the correct modification of such a result. Some applications are also given.


2020 ◽  
pp. 179-182
Author(s):  
Inas Salman Obaid ◽  
Mukdad Qaess Hussain ◽  
Darya Jabar AbdulKareem

Let be a ring with 1 and D is a left module over . In this paper, we study the relationship between essentially small quasi-Dedekind modules with scalar and multiplication modules. We show that if D is a scalar small quasi-prime -module, thus D is an essentially small quasi-Dedekind -module. We also show that if D is a faithful multiplication -module, then D is an essentially small prime -module iff is an essentially small quasi-Dedekind ring.


Author(s):  
Morou Amidou ◽  
Ousmane Moussa Tessa

In this paper, we present a dynamical method for computing the syzygy module of multivariate Laurent polynomials with coefficients in a Dedekind ring (with zero divisors) by reducing the computation over Laurent polynomial rings to calculations over a polynomial ring via an appropriate isomorphism.


2019 ◽  
Vol 19 (03) ◽  
pp. 2050043
Author(s):  
Sri Wahyuni ◽  
Hidetoshi Marubayashi ◽  
Iwan Ernanto ◽  
Sutopo

Let [Formula: see text] be a strongly graded ring of type [Formula: see text] such that [Formula: see text] is a prime Goldie ring with its quotient ring [Formula: see text]. It is shown that the following three conditions are equivalent: (i) [Formula: see text] is a [Formula: see text]-invariant generalized Dedekind ring ([Formula: see text]-Dedekind ring for short), (ii) [Formula: see text] is a [Formula: see text]-Dedekind ring and (iii) [Formula: see text] is a graded [Formula: see text]-Dedekind ring. We describe all invertible ideals of [Formula: see text]-Dedekind rings in terms of [Formula: see text] and [Formula: see text]. We provide counterexamples of [Formula: see text]-invariant [Formula: see text]-Dedekind rings which are not [Formula: see text]-Dedekind rings.


2013 ◽  
Vol 192 (2) ◽  
pp. 154-163
Author(s):  
K. O. Batalkin ◽  
N. A. Vavilov

2012 ◽  
Vol 132 (10) ◽  
pp. 2267-2276 ◽  
Author(s):  
Mohamed E. Charkani ◽  
Abdulaziz Deajim
Keyword(s):  

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