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Rings of Quotients of Rings of Derivations
Canadian Mathematical Bulletin, 1968The concept of a rational extension of a Lie module is defined as in the associative case [1, pp. 81 and 79]. It then follows from [3, Theorem 2.3] that any Lie module possesses a maximal rational extension (a rational completion), unique up to isomorphism.
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Nature Physics, 2020
Quantum cascade lasers are bright and compact semiconductor lasers that emit light in the mid- to far-infrared spectral region. The use of a closed ring cavity has now set them on the path towards ultrafast pulses.
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Quantum cascade lasers are bright and compact semiconductor lasers that emit light in the mid- to far-infrared spectral region. The use of a closed ring cavity has now set them on the path towards ultrafast pulses.
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COUNTABLE RINGS AS ENDOMORPHISM RINGS
The Quarterly Journal of Mathematics, 1988Let \(\sum \leq \prod\) be the direct sum and product of countably many copies of the integers, let \(\sum \leq D\leq \prod\) such that D/\(\sum\) is the divisible part of \(\prod /\sum\), and let \(e_ n=(\delta_{in})_{i\in {\mathbb{N}}}\in \prod\) be the generalized n-th unit vector.
Dugas, M., Irwin, J., Khabbaz, S.
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Local Rings of Rings of Quotients
Algebras and Representation Theory, 2008Let \(a\) be an element of a ring \(R\). The ring \(R_a\) that is obtained by defining on the Abelian group \((aRa,+)\) the multiplication \(axa\cdot aya=axaya\) is called the local ring of \(R\) at \(a\). This concept was introduced by K.~Meyberg in 1972 in the nonassociative context of Jordan systems.
Gómez Lozano, M. A., Siles Molina, M.
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Rings of Quotients of Group Rings
Canadian Journal of Mathematics, 1969The group ring AG of a group G and a ring A is the ring of all formal sums Σg∈G agg with ag ∈ A and with only finitely many non-zero ag. Elements of A are assumed to commute with the elements of G. In (2), Connell characterized or completed the characterization of Artinian, completely reducible and (von Neumann) regular group rings ((2) also contains ...
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On the Ring of Quotients of a Boolean Ring
Canadian Mathematical Bulletin, 1959Two important mathematical constructions are: the construction of the rational s from the integers and the construction of the reals from the rationals. The first process can be carried out for any ring, producing its maximal ring of quotients [4, 5]. The second process can be carried out for any partially ordered set producing its Dedekind-MacNeille ...
Brainerd, B., Lambek, J.
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On Deformation Rings and Hecke Rings
The Annals of Mathematics, 1996The author proves the following result: Let \(E\) be an elliptic curve defined over the rational field \(\mathbb{Q}\) with semistable reduction at the prime 3. Suppose that either \(E\) has semistable reduction at 5 or that \(\rho_{E,3}: G_{\mathbb{Q}}\to\text{GL}(2,\mathbb{F}_3)\) is absolutely irreducible when restricted to \(\text{Gal}(\overline ...
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On derivations in near-rings and rings
Mathematical Journal of Okayama University, 1992In a near-ring \(R\) a derivation \(D\) is called an scp-derivation if \([x,y] = [D(x), D(y)]\), a Daif 1(2)-derivation if \(D(xy) - D(yx) = [x, y] (=[-x, y])\) (\(\forall x, y \in R\)). Various commutativity (and distributivity) results linked to such derivations are given: e.g.
Bell, Howard E., Mason, Gordon
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Southeast Asian Bulletin of Mathematics, 2000
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