Results 91 to 100 of about 62,458 (328)
RING STRUCTURE OF INTEGER-VALUED RATIONAL FUNCTIONS
Journal of Commutative Algebra$\DeclareMathOperator{\IntR}{Int{}^\text{R}}$Integer-valued rational functions are a natural generalization of integer-valued polynomials. Given a domain $D$, the collection of all integer-valued rational functions over $D$ forms a ring extension $\IntR(D)$ of $D$. For a valuation domain $V$, we characterize when $\IntR(V)$ is a Prüfer domain and when $
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Let F:K be a Galois extension of number fields and Q a prime ideal of O_F lying over the prime P of O_K. By analyzing the Q-adic closure of O_K in O_F we characterize those rings of integers O_K for which every residue class ring of Int(O_K) modulo a non-zero prime ideal is GE2 (meaning that every unimodular pair can be trasformed to (1,0) by a series ...
Frisch, Sophie, Halter-Koch, Franz
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Rings of integer-valued rational functions
Journal of Pure and Applied Algebra, 1998 For \(D\) an integral domain with quotient field \(K\) and \(E \subseteq D\), let \(\text{Int} (E, D)= \{f \in K[x]\mid f(E) \subseteq D\}\) and \(\text{Int}^R (E, D) = \{f \in K (x) \mid f(E) \subseteq D\}\). For a large class of rings, called \(D\)-rings (which includes \({\mathbb Z}\)), \(\text{Int}^R (D, D) = \text{Int} (D, D)\).
Loper, Alan, Cahen, Paul-Jean
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Advanced Science, EarlyView.This study introduces a multifunctional hydrogel coating (Lap‐CMCSMA/GelMA@SeNPs) that scavenges ROS, modulates immune responses, and shows strong antibacterial activity. It effectively restores the peri‐implant microenvironment. The coating exhibits excellent biocompatibility and promotes osteogenic differentiation.
Su Jiang +7 more
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Signature Scheme Using the Root Extraction Problem on Quaternions
Journal of Applied Mathematics, 2014 The root extraction problem over quaternion rings modulo an RSA integer is defined, and the intractability of the problem is examined. A signature scheme is constructed based on the root extraction problem.
Baocang Wang, Yupu Hu
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Matrices over rings of algebraic integers
Linear Algebra and its Applications, 1991 For matrices over a domain R of algebraic integers the authors investigate: (i) completions, (ii) the Hermite form, (iii) the Schur form, (iv) the Smith form, and (v) links relating eigenvalues and Smith invariants. These items have been investigated previously but not in the present context.
Newman, Morris, Thompson, Robert C.
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Single‐Target Pairing System (StarPair) for Large‐Scale Interrogation of Cell–Cell Interactions
Advanced Science, EarlyView.This work presents a single‐target pairing system, StarPair, enabling cell–cell interaction studies by target combination in droplets. StarPair offers superior pairing efficiencies over 95% and operation frequencies of 105 pairs per 9.5 h for two‐target pairing, allowing large‐scale interrogation of immune cell‐cancer cell interactions and precise ...
Tianjiao Mao +6 more
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Commutativity theorems for rings with constraints on commutators
International Journal of Mathematics and Mathematical Sciences, 1991 In this paper, we generalize some well-known commutativity theorems for associative rings as follows: Let n>1, m, s, and t be fixed non-negative integers such that s≠m−1, or t≠n−1, and let R be a ring with unity 1 satisfying the polynomial identity ys[xn,
Hamza A. S. Abujabal
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K-theory for ring C*-algebras - the case of number fields with higher roots of unity
We compute K-theory for ring C*-algebras in the case of higher roots of unity and thereby completely determine the K-theory for ring C*-algebras attached to rings of integers in arbitrary number fields.Comment: 26 pages, final version, accepted for ...
L Ück, Wolfgang, Xin Li
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Factor rings of the Gaussian integers
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie, 2004 Whereas the homomorphic images of Z (the ring of integers) are well known, namely Z, {0} and Zn (the ring of integers modulo n), the same is not true for the homomorphic im-ages of Z[i] (the ring of Gaussian integers). More generally, let m be any nonzero square free integer (positive or negative), and consider the integral domain Z[ √m]={a + b √m | a,
Cody Patterson +2 more
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