169,441 research outputs found
JACOBSON RADICAL ALGEBRAS WITH QUADRATIC GROWTH
No full textWe show that over every countable algebraically closed field K there exists a finitely generated K-algebra that is Jacobson radical, infinite-dimensional, generated by two elements, graded and has quadratic growth. We also propose a way of constructing examples of algebras with quadratic growth that satisfy special types of relations.</p
Proper Ferroelectricity in the Dion?Jacobson Material CsBi2Ti2NbO10: Experiment and Theory
No full textA diverse range of materials and properties are exhibited by layered perovskites. We report on the synthesis, characterization, and computational investigation of a new ferroelectric?CsBi2Ti2NbO10, an n = 3 member of the Dion?Jacobson (DJ) family. Structural studies using variable temperature neutron powder diffraction indicate that a combination of octahedral rotations and polar displacements result in the polar structure. Density functional theory calculations reveal that the wider perovskite blocks in CsBi2Ti2NbO0 stabilize proper ferroelectricity, in contrast to the hybrid-improper ferroelectricity reported for all other DJ phases. Our results raise the possibility of a new class of proper ferroelectric materials analogous to the well-known Aurivillius phases
The Jacobson radical of rings with nilpotent homogeneous elements
No full textA result of Bergman says that the Jacobson radical of a graded algebra is homogeneous. It is shown that while graded Jacobson radical algebras have homogeneous elements nilpotent, it is not the case that graded algebras all of whose homogeneous elements are nilpotent are Jacobson radical. To contrast this, the following result of the author is slightly extended. Let R be a graded algebra generated in the degree one. If for every n, the n x n matrix algebra over R has all homogeneous elements nilpotent, then R is Jacobson radical.</p
JACOBSON RADIKAL PADA RING DAN PERLUASANNYA
No full textPada artikel ini akan diperkenalkan Jacobson radikal pada ring serta perluasannya. Jacobson radikal dari ring adalah irisan dari semua ideal maksimal di ring tersebut. Jika setiap elemen pada suatu ideal pada ring merupakan elemen nilpoten, maka ideal tersebut adalah nilradikal. Nilradikal pada suatu ring termuat pada Jacobson radikal dari ring tersebut. Pada artikel ini diasumsikan R merupakan ring komutatif dengan elemen kesatuan. Beberapa karakteristik dari J(R) adalah y∈J(R) jika dan hanya jika 1-xy merupakan suatu unit di R untuk setiap x∈R, elemen idempoten pada J(R) hanyalah nol, J(R/J(R)) =0+J(R), serta jika A⊂J(R) maka J(R/A)=J(R)/A. Jacobson radikal pada ring diperluas menjadi ring Jacobson semisimple yang selanjutnya diperluas menjadi ring Jacobson. Selain pada ring, Jacobson radikal juga diperluas pada himpunan modul, yaitu konstruksi dari Jacobson radikal pada modul dan pendefinisian modul Jacobson.
Kata kunci: Jacobson radikal, nilradikal, ring Jacobson semisimple, ring Jacobson, modul Jacobson.
This article will introduce the Jacobson radical on ring with the generalization. Jacobson radical equals intersection of all maximal ideal of the ring. If all elements of an ideal is nilpotent, then it is called nil radical. The Jacobson radical contains all nil radical. Assume the ring R is commutative with unity. Some characteristic of Jacobson radical are y∈J(R) if and only if 1-xy is a unit in R for all x∈R, 0 is the only idempotent elements in J(R), J(R/J(R)) =0+J(R), also if A⊂J(R) then J(R/A)=J(R)/A. Jacobson radical on the ring was generalized become Jacobson semisimple ring then also was generalized become ring Jacobson. Jacobson radical on ring was generalized on module too, it was construction of Jacobson radical on modules and definition of Jacobson module.
Key word: Jacobson radical, nil radical, Jacobson semisimple ring, Jacobson ring, Jacobson module
Guide to the Hjalmer Arthur Jacobson Collection
No full textSmall collection consisting of Hjalmer’s diplomas from the College of Medical Evangelists (1926, 1927), his embryology syllabus and notes, and a copy of “The Periscope” containing the portraits and history of the 1916 nursing class of Battle Creek Sanitarium. With this gift came the diploma of Ethel R. Zelker Jacobson, Hjalmer’s wife, for her completion of the nursing program at Battle Creek Sanitarium, 1918, but this diploma has gone missing
Ocyplanus megalops JACOBSON & KISTNER 1983
No full textOcyplanus megalops JACOBSON & KISTNER 1983 Ocyplanus megalops JACOBSON & KISTNER 1983: 33. M a t e r i a l:1, O. Afrika, Gomba, lux, leg. Inst. Amani (MNHUB). D i s t r i b u t i o n: Zaire, Gambia, Ivory Coast, Ghana.Published as part of Pace, R., 2012, New data and new species of Aleocharinae from Tropical Africa in the Natural History Museum of the Humboldt University, Berlin (Coleoptera, Staphylinidae), pp. 1331-1362 in Linzer biologische Beiträge 44 (2) on page 1342, DOI: 10.5281/zenodo.533529
Classification of rings with toroidal Jacobson graph
No full textsummary:Let be a commutative ring with nonzero identity and the Jacobson radical of . The Jacobson graph of , denoted by , is defined as the graph with vertex set such that two distinct vertices and are adjacent if and only if is not a unit of . The genus of a simple graph is the smallest nonnegative integer such that can be embedded into an orientable surface . In this paper, we investigate the genus number of the compact Riemann surface in which can be embedded and explicitly determine all finite commutative rings (up to isomorphism) such that is toroidal
Extensões polinomiais e anéis de Jacobson
No full textOrientador: Prof. Dr. Laerte BemmDissertação (mestrado em Matemática)--Universidade Estadual de Maringá, Dep. de Matemática, Programa de Pós-Graduação em Matemática, Área de Concentração: Álgebra, 2019Resumo: Neste trabalho iremos demonstrar um resultado, devido J. F. Watters, que diz que um anel R é um anel de Jacobson se, e só se, o anel de polinômios R[x] é um anel de Jacobson. Teremos como um segundo objetivo demonstrar um resultado análogo ao obtido por Watters, para os skew anéis de polinômios. Provaremos que um anel R é Jacobson se, e somente se, o skew anel de polinômios R[x; ] é Jacobson, este resultado é devido a K. R. Pearson, W. Stephenson e J. F. Watters.Abstract: In this work we will prove a result, due to J. F. Watters, which says that a ring R
is a Jacobson ring if and only if the polynomial ring R[x] is a Jacobson ring. We will have as a second objective to demonstrate a result analogous to that one obtained by Watters, for skew polynomials rings. We will prove that a ring R is -Jacobson if, and only if, the skew polynomials ring R[x; ] is -Jacobson, this result is due to K. R. Pearson, W. Stephenson and J F Watters
Transient evoked otoacoustic emission-basedscreening in typical nurseries: A response to Jacobson and Jacobson
No full textJacobson and Jacobson (Int. J. Pediatr. Otorhinolaryngol. 29 (1994) 235-248) recently questioned whether TEOAE-based newborn hearing screening similar to what was recommended by the National Institutes of Health could be implemented in a typical nursery setting. They concluded that, \u27the theoretical advantage of TEOAEs as a method for screening newborn babies at risk for hearing loss may not be realized in acute practice.\u27 This article presents data based on dozens of currently operational TEOAE-based newborn hearing screening programs which demonstrate that the concerns raised by Jacobson and Jacobson are not representative of what is being experienced by operational newborn hearing screening programs
The Jacobson radical of the endomorphism ring of a projective module.
No full textIn a recently published paper [3], the elements of the Jacobson radical of a ring of row-finite matrices over an arbitrary ring
R
R
are characterized as those matrices with entries in the Jacobson radical of
R
R
which have a vanishing set of column ideals. In this paper, the characterization is extended to include the endomorphism ring of an arbitrary projective module. In the process we offer a greatly simplified proof of the theorem for row-finite matrices.</p
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