Results 231 to 240 of about 32,028 (266)

On Partially Ordered Rings

Journal of Mathematical Sciences, 2018
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Tiled Orders and Frobenius Rings

Mathematical Notes, 2002
Let \(R\) be a discrete valuation ring with quotient field \(K\) and \({\mathfrak p}:=\text{Rad\,}R\). For an \(R\)-order \(\Lambda\) in a symmetric \(K\)-algebra \(A\), the \((\Lambda,\Lambda)\)-bimodules \(\Lambda\) and \(\Lambda^*:=\hom_R(\Lambda,R)\) can be regarded as full \(R\)-lattices in \(A\).
Dokuchaev, M. A., Kirichenko, V. V., Chernousova, Zh. T.   +2 more
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REAL CLOSED RINGS AND ORDERED VALUATION RING

Mathematical Logic Quarterly, 1983
The article contains some model theoretic results on real closed rings and ordered valuation rings, supplementing the work of Cherlin and Dickmann on the same subject. The results confirm the analogy between real closed rings and real closed fields. There is a minor error in Proposition 1.9 which is part of Theorem 1.
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Quotient Rings of a Class of Lattice-Ordered-Rings

Canadian Journal of Mathematics, 1973
An f-ring R with zero right annihilator is called a qf-ring if its Utumi maximal left quotient ring Q = Q(R) can be made into and f-ring extension of R. F. W. Anderson [2, Theorem 3.1] has characterized unital qf-rings with the following conditions: For each q ∈ Q and for each pair d1, d2 ∈ R+ such that diq ∈ R(i) (d1q)+ Λ (d2q)- = 0, and(ii) d1 Λ d2 =
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Differentiation for Orders and Artinian Rings

Algebras and Representation Theory, 2004
Let \(R\) be a complete valuation domain. Given an \(R\)-order \(\Lambda\), we denote by \(\Lambda\text{-lat}\) the category of left \(\Lambda\)-lattices, that is, finitely generated left \(\Lambda\)-modules that are \(R\)-free. In his recent papers [J. Pure Appl. Algebra 153, No. 2, 171-190 (2000; Zbl 0964.16016) and Colloq. Math. 89, No.
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STRAIGHT LEFT ORDERS IN RINGS

The Quarterly Journal of Mathematics, 1992
In an earlier work [Commun. Algebra 18, 3085-3110 (1990; Zbl 0719.16022)] the authors introduced a notion of order such that inverses are taken in every maximal subgroup of the ring of quotients, not only in its unit group (which may not even exist in this case).
Fountain, John, Gould, Victoria
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Noetherian Rings Whose Factor Rings are Orders in Artinian Rings

Journal of the London Mathematical Society, 1986
A ring R is said to be q-Artinian if every factor ring of R has an Artinian quotient ring. The main result of this paper is that a left and right Noetherian P.I. ring R is q-Artinian if and only if R is a direct sum of rings each of which is either Artinian or prime of Krull dimension 1.
Armendariz, Efraim P., Hajarnavis, C. R.
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$P$-orderings of noncommutative rings

Proceedings of the American Mathematical Society, 2015
Let \(K\) 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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A Note on a Fully Ordered Ring

Canadian Mathematical Bulletin, 1967
A ring R (associative ring) is said to be fully ordered provided that R is a linearly ordered set under a relation such that for any a, b and c in R, implies that and if c ε 0 then and . We say a subset K of R is convex provided that if a, b ε K such that then the interval [a, b] is a subset of K. Obviously an additive subgroup K of R is convex if
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Priestley Rings and Priestley Order-Compactifications

Order, 2010
The authors study partially ordered sets by introducing the concept of Priestley rings of upsets. They prove that the family of non-equivalent Priestley ring representations of a distributive lattice can be put in bijection with the family of dense subspaces of the Priestley space of the given lattice.
Guram Bezhanishvili, Patrick J. Morandi
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