Results 221 to 230 of about 1,200,355 (273)
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$P$-orderings of noncommutative rings
Proceedings of the American Mathematical Society, 2015Let \(K\) be a local field with valuation \(\nu\), \(D\) a division algebra over \(K\) to which \(\nu\) extends, \(R\) the maximal order in \(D\) with respect to \(\nu\) and \(S\) a subset of \(R\). If \(D[x]\) denotes the ring of polynomials over \(D\) with \(x\) a central variable, then the set of integer valued polynomials on \(S\) is \(\text{Int}(S,
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Comultiplication Modules over Noncommutative Rings
Journal of Mathematical Sciences, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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LCD and ACD codes over a noncommutative non-unital ring with four elements
Cryptography and Communications, 2021Minjia Shi +3 more
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LINEAR RECURRING SEQUENCES OVER NONCOMMUTATIVE RINGS
Journal of Algebra and Its Applications, 2012Contrary to the commutative case, the set of linear recurring sequences with values in a module over a noncommutative ring is no more a module for the usual operations. We show the stability of these operations when the ring is a matrix ring or a division ring. In the case of a finite dimensional division ring over its center, we give an algorithm for
Cherchem, Ahmed +2 more
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Noncommutative Valuation Rings
1988Various possible versions of noncommutative valuation rings and their applications are discussed.
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Noncommutative elementary divisor rings
Ukrainian Mathematical Journal, 1988The main results are the following: Theorem 7. Let R be a Bezout domain and for every finite set \(a_ 1,a_ 2,..\). of non-factorial elements of R there exist an \(a\in R\), such that \(aR=Ra\) and \(a_ i=af_ i\) for a factorial \(f_ i\). Then R is an elementary divisor domain. Theorem 8.
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On noncommutative Gröbner bases over rings
Journal of Mathematical Sciences, 2007Let \(R\) be a commutative ring with unity. It was recently proved by the author that inside the polynomial ring \(R[x_1,\dots,x_n]\) the following criterion is true: \(R\) is an arithmetical ring iff in order to verify that a given set of polynomials \(\{f_\alpha\}\) is a Gröbner basis of the ideal generated by this set it is sufficient to show that \(
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Modules over Noncommutative Rings
2006This chapter contains two sets of tools for working with modules over a ring R with identity. The first set concerns finiteness conditions on modules, and the second set concerns the Hom and tensor product functors.
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Weierstrass preparation theorem for noncommutative rings
Journal of Mathematical Sciences, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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