Extracta Mathematica Vol. 34, nº 1 (2019)http://hdl.handle.net/10662/97272020-01-21T14:02:40Z2020-01-21T14:02:40ZAdditivity of elementary maps on gamma ringsMacedo Ferreira, Bruno L.http://hdl.handle.net/10662/99922019-11-13T12:54:50Z2019-01-01T00:00:00ZAdditivity of elementary maps on gamma rings
Macedo Ferreira, Bruno L.
Let M and M' be Gamma rings, respectively. We study the additivity of surjective elementary maps of M ⨉ M'. We prove that if M contains a non-trivial γ-idempotent satisfying some conditions, then they are additive.
2019-01-01T00:00:00ZNon-additive Lie centralizer of strictly upper triangular matricesAhmed, Driss Aiat Hadjhttp://hdl.handle.net/10662/99832019-11-13T08:36:53Z2019-01-01T00:00:00ZNon-additive Lie centralizer of strictly upper triangular matrices
Ahmed, Driss Aiat Hadj
Let ℱ be a field of zero characteristic, let Nn(ℱ) denote the algebra of n X n strictly upper triangular matrices with entries in ℱ, and let ƒ : Nₙ(ℱ) → Nₙ(ℱ) be a non-additive Lie centralizer of Nₙ(ℱ), that is, a map satisfying that ƒ([X; Y ]) = [ƒ(X); Y ] for all X; Y ∈ Nₙ(ℱ). We prove that ƒ(X) = ⋋ X + ƞ (X) where ⋋ ∈ ℱ and ƞ is a map from Nₙ(ℱ) into its center Ƶ (Nₙ(F)) satisfying that ƞ([X; Y ]) = 0 for every X; Y in Nₙ(ℱ).
2019-01-01T00:00:00ZTetrahedral chains and a curious semigroupStewart, Ianhttp://hdl.handle.net/10662/99822019-11-13T08:39:04Z2019-01-01T00:00:00ZTetrahedral chains and a curious semigroup
Stewart, Ian
In 1957 Steinhaus asked for a proof that a chain of identical regular tetrahedra joined face to face cannot be closed. Swierczkowski gave a proof in 1959. Several other proofs are known, based on showing that the four reections in planes though the origin parallel to the faces of the tetrahedron generate a group ℛ isomorphic to the free product ℤ₂ ∗ ℤ₂ ∗ ℤ₂ ∗ ℤ₂. We relate the reections to elements of a semigroup of 3 X 3 matrices over the finite field ℤ₃, whose structure provides a simple and transparent new proof that ℛ is a free product. We deduce the non-existence of a closed tetrahedral chain, prove that ℛ is dense in the orthogonal group O(3), and show that every ℛ-orbit on the 2-sphere is equidistributed.
2019-01-01T00:00:00ZCharacterizations of minimal hypersurfaces immersed in certain warped productsLima, Eudes L. deLima, Henrique F. deLima, Eraldo A.Medeiros, Adriano A.http://hdl.handle.net/10662/99812019-11-13T08:33:23Z2019-01-01T00:00:00ZCharacterizations of minimal hypersurfaces immersed in certain warped products
Lima, Eudes L. de; Lima, Henrique F. de; Lima, Eraldo A.; Medeiros, Adriano A.
Our purpose in this paper is to investigate when a complete two-sided hypersurface immersed with constant mean curvature in a Killing warped product Mⁿ X ⍴ℝ, whose Riemannian base Mⁿ has sectional curvature bounded from below and such that the warping function ⍴ ∈ C∞(M) is supposed to be concave, is minimal (and, in particular, totally geodesic) in the ambient space. Our approach is based on the application of the well known generalized maximum principle of Omori-Yau.
2019-01-01T00:00:00Z