Simple reduction theorems for extension and torsion functors

1961 ◽  
Vol 57 (3) ◽  
pp. 483-488
Author(s):  
D. G. Northcott
Keyword(s):  
Commutative Ring ◽  
Zero Divisor ◽  
Residue Class ◽  
Identity Element ◽  
Negative Integer ◽  
Reduction Theorem ◽  
Residue Class Ring ◽  
Image Position ◽  
Class Ring ◽  
Simple Reduction

Let Λ be a commutative ring with an identity element and c an element of Λ which is not a zero divisor Denote by Ω the residue class ring Λ/Λc. If now M is a Λ-module for which c is not a zero divisor, and A is an Ω-module, then a theorem of Rees (2) asserts that, for every non-negative integer n, we have a Λ-isomorphismThis reduction theorem has found a number of useful and interesting applications.

scholarly journals Permutation polynomials in several variables over residue class rings

1987 ◽  
Vol 43 (2) ◽  
pp. 171-175 ◽  
Author(s):  
H. K. Kaiser ◽  
W. Nöbauer
Keyword(s):  
Commutative Ring ◽  
Residue Class ◽  
Polynomial Function ◽  
Permutation Polynomial ◽  
Permutation Polynomials ◽  
Several Variables ◽  
Residue Class Ring ◽  
Class Ring

AbstractThe concept of a permutation polynomial function over a commutative ring with 1 can be generalized to multiplace functions in two different ways, yielding the notion of a k-ary permutation polynomial function (k > 1, k ∈ N) and the notion of a strict k-ary permutation polynomial function respectively. It is shown that in the case of a residue class ring Zm of the integers these two notions coincide if and only if m is squarefree.

Residually Finite Rings

1970 ◽  
Vol 22 (1) ◽  
pp. 92-101 ◽  
Author(s):  
Kim Lin Chew ◽  
Sherry Lawn
Keyword(s):  
Commutative Ring ◽  
Homomorphic Image ◽  
Finite Index ◽  
Residue Class ◽  
Finite Rings ◽  
Residually Finite ◽  
Residue Class Ring ◽  
Class Ring ◽  
Equivalent Conditions

Throughout this paper a ring will always be an associative, not necessarily commutative ring with an identity. It is tacitly assumed that the identity of a subring coincides with that of the whole ring. A ring R is said to be residually finite if it satisfies one of the following equivalent conditions:(1) Every non-zero ideal of R is of finite index in R;(2) For each non-zero ideal A of R, the residue class ring R/A is finite;(3) Every proper homomorphic image of R is finite.The class of residually finite rings is large enough to merit our investigation. All finite rings and all simple rings are trivially residually finite. Other residually finite rings are said to be proper.

scholarly journals The zero-divisor Cayley graph of the residue class ring $\left( {{Z}_{n}},\oplus ,\odot \right)$

2019 ◽  
Vol 7 (3) ◽  
pp. 590-594
Author(s):  
Jangiti Devendra ◽  
Levaku Madhavi ◽  
Tippaluri Nagalakshumma
Keyword(s):  
Cayley Graph ◽  
Zero Divisor ◽  
Residue Class ◽  
Residue Class Ring ◽  
Class Ring

scholarly journals Sums of generators of ideals in residue class ring

2017 ◽  
Vol 174 ◽  
pp. 14-25 ◽  
Author(s):  
Xin Zhang ◽  
Chun-Gang Ji
Keyword(s):  
Residue Class ◽  
Residue Class Ring ◽  
Class Ring

scholarly journals Normalité de certains anneaux déterminantiels quantiques

1999 ◽  
Vol 42 (3) ◽  
pp. 621-640 ◽  
Author(s):  
Laurent Rigal
Keyword(s):  
Residue Class ◽  
Quantum Algebras ◽  
Regular Functions ◽  
Maximal Orders ◽  
Ring Of Fractions ◽  
Prime Factors ◽  
The Matrix ◽  
Residue Class Ring ◽  
Class Ring ◽  
The Ideal

Let Kq[X] = Oq(M(m, n)) be the quantization of the ring of regular functions on m × n matrices and Iq (X) be the ideal generated by the 2 × 2 quantum minors of the matrix X=(Xij)l≤i≤m, I≤j≤n of generators of Kq[X]. The residue class ring Rq(X) = Kq[X]/Iq(X) (a quantum analogue of determinantal rings) is shown to be an integral domain and a maximal order in its divisionring of fractions. For the proof we use a general lemma concerning maximalorders that we first establish. This lemma actually applies widely to prime factors of quantum algebras. We also prove that, if the parameter isnot a root of unity, all the prime factors of the uniparameter quantum space are maximal orders in their division ring of fractions.

scholarly journals New Generalized Cyclotomic Quaternary Sequences with Large Linear Complexity and a Product of Two Primes Period

Information ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 193
Author(s):  
Jiang Ma ◽  
Wei Zhao ◽  
Yanguo Jia ◽  
Haiyang Jiang
Keyword(s):  
Spectral Sequence ◽  
Linear Complexity ◽  
Residue Class ◽  
Important Criterion ◽  
Random Sequences ◽  
Gray Mapping ◽  
Quaternary Sequences ◽  
Hamming Weights ◽  
Residue Class Ring ◽  
Class Ring

Linear complexity is an important criterion to characterize the unpredictability of pseudo-random sequences, and large linear complexity corresponds to high cryptographic strength. Pseudo-random Sequences with a large linear complexity property are of importance in many domains. In this paper, based on the theory of inverse Gray mapping, two classes of new generalized cyclotomic quaternary sequences with period pq are constructed, where pq is a product of two large distinct primes. In addition, we give the linear complexity over the residue class ring Z4 via the Hamming weights of their Fourier spectral sequence. The results show that these two kinds of sequences have large linear complexity.

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