Results 1 to 10 of about 10,009 (83)

Commutative Division Ring and Skew Field on the Binomial Coefficients of Combinatorial Geometric Series

, 2022
This paper discusses an abelian group, ring, and field under addition and multiplication of the binomial coefficients in combinatorial geometric series. The coefficient for each term in combinatorial geometric series refers to a binomial coefficient. This idea can enable the scientific researchers to solve the real life problems.
openaire   +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

Simple Rings and Degree Maps [PDF]

, 2013
For an extension A/B of neither necessarily associative nor necessarily unital rings, we investigate the connection between simplicity of A with a property that we call A-simplicity of B.
Nystedt, Patrik, Öinert, Johan
core   +1 more source

Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras

, 2013
The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings
A. Kandri-Rody, A. Leroy, A. Quadrat, B. Beckermann, B. Strenström, D. Andres, D. Grigoriev, D. Robertz, F. Chyzak, F. Chyzak, F.W. Anderson, G. Bergman, H. Gluesing-Luerssen, J. Apel, J. Apel, J. Gómez-Torrecillas, J. Gómez-Torrecillas, J. Gómez-Torrecillas, J. Gómez-Torrecillas, J.-E. Björk, J.C. McConnell, J.E. Björk, J.L. Bueso, J.L. Bueso, J.L. Bueso, J.L. Bueso, J.L. Bueso, J.L. Bueso, L. Robbiano, M. Barakat, M. Bronstein, M. Giesbrecht, M. Giesbrecht, M. Hazewinkel, M. Hoeij Van, M. Put Van der, M. Saito, M.A. Barkatou, M.F. Singer, N. Jacobson, N. Jacobson, N. Jacobson, O. Lezama, P.J. Hilton, R.C. Churchill, T. Cluzeau, T. Mora, T. Mora, V. Levandovskyy, V. Levandovskyy, V. Levandovskyy, V. Weispfenning, V.P. Gerdt, W. Adams, Ø. Ore   +54 more
core   +1 more source

Free structures in division rings

, 2013
Makar-Limanov's conjecture states that if a division ring D is finitely generated and infinite dimensional over its center k then D contains a free k-subalgebra of rank 2.
Júnior, Renato Fehlberg
core   +1 more source

Computing the bound of an Ore polynomial. Applications to factorization

, 2018
We develop a fast algorithm for computing the bound of an Ore polynomial over a skew field, under mild conditions. As an application, we state a criterion for deciding whether a bounded Ore polynomial is irreducible, and we discuss a factorization ...
Gomez-Torrecillas, Jose, Lobillo, F. J., Navarro, Gabriel   +2 more
core   +1 more source

Weighted noncommutative regular projective curves

, 2016
Let $\mathcal{H}$ be a noncommutative regular projective curve over a perfect field $k$. We study global and local properties of the Auslander-Reiten translation $\tau$ and give an explicit description of the complete local rings, with the involvement of
Kussin, Dirk
core   +1 more source

The structure of finite meadows [PDF]

, 2009
A meadow is a commutative ring with a total inverse operator satisfying 0^{-1}=0. We show that the class of finite meadows is the closure of the class of Galois fields under finite products.
Bethke, Inge, Rodenburg, Piet, Sevenster, Arjen   +2 more
core   +2 more sources

Skew and linearized Reed-Solomon codes and maximum sum rank distance codes over any division ring

, 2018
Reed-Solomon codes and Gabidulin codes have maximum Hamming distance and maximum rank distance, respectively. A general construction using skew polynomials, called skew Reed-Solomon codes, has already been introduced in the literature.
Martínez-Peñas, Umberto
core   +1 more source