Results 71 to 80 of about 199,681 (176)
Uniserial Rings and Skew Polynomial Rings
Tokyo Journal of Mathematics, 1984 If \(\tau\) is an automorphism of a division ring D then, for each positive integer c, the factor ring \(S/x^ cS\) of the skew polynomial ring \(S=D[x;\tau]\) is a local uniserial ring of split type. The purpose of this paper is to establish a necessary and sufficient condition on a local uniserial ring R for R to be isomorphic to a ring of the above ...
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Research on algorithms of data encryption scheme that supports homomorphic arithmetical operations
Tongxin xuebao, 2015 An efficient homomorphic encryption scheme called CESIL was proposed to meet the requirements of operating on encrypted data when protecting users' privacy in computing services.CESIL included key generation algorithm,encryption algorithm,decryption ...
ANGPan Y +5 more
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More on Codes Over Finite Quotients of Polynomial Rings
IEEE AccessLet $q=p^{r}$ be a prime power, ${\mathbb {F}}_{q}$ be the finite field of order q and $f(x)$ be a monic polynomial in ${\mathbb {F}}_{q}[x]$ . Set ${\mathbb {A}}:={\mathbb {F}}_{q}[x]/{\left \lt {{ f(x) }}\right \gt }$ .
Emad Kadhim Al-Lami +3 more
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Polynomial rings over a Hilbert ring.
Michigan Mathematical Journal, 1984 A commutative ring R with identity is called a Hilbert ring if every prime ideal of R is an intersection of maximal ideals. The paper discusses some open questions surrounding an incorrect result by R. Gilmer, which asserts that if R is a Hilbert ring and if \(\{X_{\lambda}\}_{\lambda \in \Lambda}\) is an infinite set of indeterminates such that for ...
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Jordan derivations of polynomial rings
Karpatsʹkì Matematičnì Publìkacìï, 2009 We study connections between the set of Jordan derivations of aring $R$ and the sets of Jordan derivations of a polynomial ring$R[x_1,dots,x_n]$ and formal power series ring$R[[x_1,dots,x_n]]$.
I. I. Lishchynsky
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About j{\mathscr{j}}-Noetherian rings
Open MathematicsLet RR be a commutative ring with identity and j{\mathscr{j}} an ideal of RR. An ideal II of RR is said to be a j{\mathscr{j}}-ideal if I⊈jI\hspace{0.33em} \nsubseteq \hspace{0.33em}{\mathscr{j}}.
Alhazmy Khaled +3 more
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Monomial retracts of polynomial rings are polynomial rings
Let $R$ be a ring and $B = R[X_1, \dots, X_n]$ the polynomial ring in $n$ variables over $R$. In this article, we consider retractions $φ: B \longrightarrow B$ such that $φ(X_i)$ is either a monic monomial or $0$. We prove that if $R$ is an integral domain, then any such retract is isomorphic to $R^{[p]}$, the polynomial ring in $p$ variables over $R$,
Chakraborty, Sagnik, Pal, Madhuparna
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Explicit formulas for chromatic polynomials of some series-parallel graphs
Учёные записки Казанского университета: Серия Физико-математические науки, 2018 The main goal of our paper is to present explicit formulas for chromatic polynomials of some planar series-parallel graphs (sp-graphs). The necklace-graph considered in this paper is the simplest non-trivial sp-graph.
E.Yu. Lerner, S.A. Mukhamedjanova
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