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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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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 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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Dual rings and cogenerator rings
Mathematical Journal of Okayama University, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Continuous Rings and Rings of Quotients
Canadian Mathematical Bulletin, 1978Throughout R will denote an associative ring with identity. Let Zℓ(R) be the left singular ideal of R. It is well known that Zℓ(R) = 0 if and only if the left maximal ring of quotients of R, Q(R), is Von Neumann regular. When Zℓ(R) = 0, q(R) is also a left self injective ring and is, in fact, the injective hull of R.
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Southeast Asian Bulletin of Mathematics, 2000
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