Results 161 to 170 of about 5,631 (197)

Algebraicity in local rings

Journal of Mathematical Sciences, 2009
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On the Deformation of Rings and Algebras

The Annals of Mathematics, 1964
CHAPTER I. The deformation theory for algebras 1. Infinitesimal deformations of an algebra 2. Obstructions 3. Trivial deformations 4. Obstructions to derivations and the squaring operation 5. Obstructions are cocycles 6. Additivity and integrability of the square 7. Restricted deformation theories and their cohomology theories 8.
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Quiver Generalized Weyl Algebras, Skew Category Algebras and Diskew Polynomial Rings [PDF]

Mathematics in Computer Science, 2017
The aim of the paper is to introduce new large classes of algebras—quiver generalized Weyl algebras, skew category algebras, diskew polynomial rings and skew semi-Laurent polynomial ...
V V Bavula
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Algebraic Elements in Group Rings

Proceedings of the American Mathematical Society, 1990
In this brief note, we study algebraic elements in the complex group algebra C
Passi, I. B. S., Passman, D. S.
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DERIVATION ALGEBRAS OF RINGS RELATED TO HEISENBERG ALGEBRAS

Journal of Algebra and Its Applications, 2004
In this paper, we will determine the Lie algebra of derivations of rings which are generalizations of the enveloping algebras of Heisenberg Lie algebras. First, we will determine which derivations are X-inner and also determine which elements in the Martindale quotient ring induce X-inner derivations.
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Ring Isomorphisms of Banach Algebras

Canadian Journal of Mathematics, 1954
In discussing an isomorphism between two Banach algebras, one will ordinarily tacitly assume that the mapping is linear (i.e., preserves the complex scalars as well as the ring operations). In general this cannot be avoided; for instance if the two Banach algebras are just the field of complex numbers, then the isomorphism is unrestricted, and could be
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Rings and Algebras

2017
A (unitary) ring is a triple (R, α, μ) where (R, α) is an abelian group whose operation α is written additively (α(r, s) = r + s) with neutral element 0 R , and (R, μ) is monoid, written multiplicatively \( ({\mu}(r, s) = {r}\cdot{s})\) with multiplicative neutral element 1 R such that these operations are coupled by distributivity, i.e., \( (r + s ...
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Algebraically Closed Regular Rings

Canadian Journal of Mathematics, 1974
In this paper all rings are commutative and have a unity. All ring homomorphisms preserve the unity. We let L denote the standard language for rings with two distinct constants, 0 and 1, playing the role of the zero and the unity respectively. A ring is regular if it satisfies the axiom (∀r) (∃r′)(rr′r = r) and it is algebraically closed if, for each ...
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Ring Derivations on Function Algebras

Canadian Mathematical Bulletin, 1990
AbstractIn this paper we show that a ring derivation on a function algebra is trivial provided that the Choquet boundary of the algebra contains a dense sequentially non-isolated set.
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ON THE HOPF ALGEBRA OF A LOCAL RING

Mathematics of the USSR-Izvestiya, 1974
The Hopf algebra TorA(k,k), where A is a local ring and k its residue class field, is studied by means of the Eilenberg-Moore spectral sequence converging to it and to a quotient algebra. It is shown that the Poincare series of A depends only on the homology structure of its Koszul complex as an algebra with Massey operations.
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