Results 31 to 40 of about 3,398,533 (269)
IEEE Access, 2020 Let F2(m) be a finite field of 2m elements, λ and k be integers satisfying λ, k ≥ 2 and denote R = F2(m)[u]/(u2λ). Let δ, α ∈ F2(m)×.
Yuan Cao +4 more
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On finiteness of chains of intermediate rings [PDF]
Monatshefte für Mathematik, 2009 Let \(R\subseteq S\) be an extension of integral domains. This extension is said to have the ``finite length of intermediate chains of domains'' property (FICP) if each chain of intermediate rings between \(R\) and \(S\) is finite. Let \(T\) be a ring between \(R\) and \(S\). Certainly if \(R\subseteq S\) has FICP, so do the extensions \(R\subseteq T\)
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LCD codes over finite chain rings
Finite Fields and Their Applications, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiusheng Liu, Hualu Liu
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On classification of finite commutative chain rings
AIMS Mathematics, 2022 <abstract><p>Let $ R $ be a finite commutative chain ring with invariants $ p, n, r, k, m. $ It is known that $ R $ is an extension over a Galois ring $ GR(p^n, r) $ by an Eisenstein polynomial of some degree $ k $. If $ p\nmid k, $ the enumeration of such rings is known.
Sami Alabiad, Yousef Alkhamees
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Advances in Mechanical Engineering, 2019 Crack initiation characteristics of ring chain of heavy-duty scraper conveyor under time-varying loads were investigated in this study. The dynamic tension of ring chain of the heavy-duty scraper conveyor was obtained using the time-varying dynamic ...
Dagang Wang +4 more
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Repeated-Root Constacyclic Codes Over the Chain Ring Fpm[u]/⟨u3⟩
IEEE Access, 2020 Let Z = Fpm[u]/(u3) be the finite commutative chain ring, where p is a prime, m is a positive integer and Fpm is the finite field with pm elements. In this paper, we determine all repeated-root constacyclic codes of arbitrary lengths over Z and their ...
Tania Sidana, Anuradha Sharma
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DNA Codes Over the Ring F₄[
IEEE Access, 2020 In this paper, we develop the method for constructing DNA codes of odd length over the finite chain ring $R=\mathbb {F}_{4}[u]/\langle u^{3}\rangle $ , which plays an important role in genetics, bioengineering and DNA computing.
Jie Liu, Hualu Liu
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Bounds on Covering Radius of Some Codes Over F₂ + uF₂ + vF₂ + uvF₂
IEEE Access, 2021 Let $R=\mathbb {F}_{2}+u\mathbb {F}_{2}+v\mathbb {F}_{2}+uv\mathbb {F}_{2}$ be a finite non-chain ring, where $u^{2}=u$ , $v^{2}=v$ , $uv=vu$ . We give the lower and upper bounds on the covering radius of different types of repetition codes for ...
Fanghui Ma, Jian Gao
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On the groups of units of finite commutative chain rings
Finite Fields and Their Applications, 2003 A commutative chain ring is a commutative ring whose ideals form a chain under set theoretic inclusion. Let \(M\) be the maximal ideal of a finite commutative chain ring \(R\) with characteristic \(p^n\), then \(R/M\) is a finite field, say \(R/M \cong \text{GF}(p^r)\), and \(pR=M^e\), \(e \leq s\), where \(s\) is the nilpotency of \(M\).
Hou, Xiang-Dong +2 more
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On J-Diagrams for the One Groups of Finite Chain Rings
Symmetry, 2023 Let R be a finite commutative chain ring with invariants p,n,r,k,m. The purpose of this article is to study j-diagrams for the one group H=1+J(R) of R, where J(R)=(π) is Jacobson radical of R. In particular, we prove the existence and uniqueness of j-diagrams for such one group.
Sami Alabiad, Yousef Alkhamees
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