Results 1 to 10 of about 50,680 (193)

Finite Dimensional Subalgebras in Matrix Rings Over Transcendental Division Algebras [PDF]

Proceedings of the American Mathematical Society, 1989
We prove in this article that for some classes of division algebras D D over a field F F every finite dimensional semisimple subalgebra of D n × n {D^{n \times n}} must be conjugate to a subalgebra of
Lichtman, A. I., Wehrfritz, B. A. F.
  +4 more sources

Creation of Low-Loss Triple-Ring Optical Filter via Direct Binary Search Inverse Design [PDF]

Sensors
This paper presents a triple-ring optical filter designed through direct binary search inverse design, comprising three cascaded rings in an add–drop configuration.
Yuchen Hu, Tong Wang, Wen Zhou, Bo Hu
doaj   +2 more sources

Valuation rings in finite-dimensional division algebras

Journal of Algebra, 1989
By a valuation ring in a division algebra \(D\) the authors understand a subring containing for each \(x\) in \(D\) either \(x\) or \(x^{-1}\). Let \(D\) be a division algebra of dimension \(n^ 2\) over its centre \(K\) and let \(B\) be a valuation ring in \(K\).
Brungs, H.H, Gräter, Joachim
openaire   +3 more sources

Even-order subgroups of finite-dimensional division rings

Journal of Algebra, 1977
Let K be a field. A finite group G is called K-adequate if there exists a K-division ring D (a finite-dimensional division algebra central over K) such that G is contained in D*, the multiplicative group of nonzero elements of D. Fein and Schacher have investigated the problem of determining for which fields K there exists a noncyclic group of odd ...
Gary Greenfield
openaire   +3 more sources

A Combinatorial Discussion on Finite Dimensional Leavitt Path Algebras [PDF]

, 2012
Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings.
Esin, Songul, Esin, Songül, Guloglu, Ismail, Güloğlu, Ismail, Kanuni, Muge, Kanuni, Müge, Koc, Ayten, Koç, Ayten   +7 more
core   +2 more sources

Fields and rings with few types [PDF]

, 2011
Let R be an associative ring with possible extra structure. R is said to be weakly small if there are countably many 1-types over any finite subset of R. It is locally P if the algebraic closure of any finite subset of R has property P.
Cohn, Cédric Milliet, Evans, Herstein, Kim, Krupiński, Milliet, Pillay, Poizat, Poizat, Wagner, Wagner, Wagner, Wagner   +13 more
core   +2 more sources

Semifields from skew polynomial rings [PDF]

, 2012
Skew polynomial rings were used to construct finite semifields by Petit in 1966, following from a construction of Ore and Jacobson of associative division algebras.
Lavrauw, Michel, Sheekey, John
core   +4 more sources

Factorizations of Elements in Noncommutative Rings: A Survey [PDF]

, 2016
We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations.
A Geroldinger, A Leroy, A Loewy, AW Chatters, AW Chatters, D Bachman, D Haile, D Lissner, D Smertnig, DA Jordan, DR Estes, DR Estes, DR Estes, DR Estes, E Hallouin, E Jespers, E Jespers, E Landau, G Grätzer, G Hegedüs, G Hegedüs, GQ Abbasi, H Cohn, H Fitting, H Marubayashi, H-H Brungs, I Gelfand, J Bergen, J Delenclos, J Towber, JH Conway, KR Goodearl, L Bruyn Le, M Chamarie, M-F Vignéras, MP Gilchrist, NR Baeth, NR Baeth, PM Cohn, PM Cohn, PM Cohn, PM Cohn, PM Cohn, PM Cohn, PM Cohn, PM Cohn, RA Beauregard, RA Beauregard, RA Beauregard, RA Beauregard, RA Beauregard, RA Beauregard, RA Beauregard, RA Beauregard, RA Beauregard, TY Lam, V Retakh   +56 more
core   +1 more source

Valued Graphs and the Representation Theory of Lie Algebras [PDF]

, 2011
Quivers (directed graphs) and species (a generalization of quivers) and their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra.
Assem, Auslander, Benson, Bourbaki, Brauer, Chen, Deng, Drinfel’d, Drozd, Gabriel, Jacobson, Lam, Lusztig, Ringel, Weil   +14 more
core   +3 more sources

Creation of Low-Loss Dual-Ring Optical Filter via Temporal Coupled Mode Theory and Direct Binary Search Inverse Design

Photonics
We propose a dual-ring optical filter based on direct binary search inverse design. The proposed device comprises two cascaded rings in an add–drop configuration.
Yuchen Hu, Tong Wang, Wen Zhou, Bo Hu
doaj   +1 more source