ON MINIMAL SETS OF -MATRICES WHOSE PAIRWISE PRODUCTS FORM A BASIS FOR

2018 ◽  
Vol 98 (3) ◽  
pp. 402-413 ◽  
Author(s):  
W. E. LONGSTAFF
Keyword(s):  
Matrix Algebra ◽  
Full Matrix ◽  
Full Matrix Algebra ◽  
The Third ◽  
Minimal Sets

Three families of examples are given of sets of $(0,1)$-matrices whose pairwise products form a basis for the underlying full matrix algebra. In the first two families, the elements have rank at most two and some of the products can have multiple entries. In the third example, the matrices have equal rank $\!\sqrt{n}$ and all of the pairwise products are single-entried $(0,1)$-matrices.

Simple Algebras Over Rational Function Fields

1979 ◽  
Vol 31 (4) ◽  
pp. 831-835 ◽  
Author(s):  
T. Nyman ◽  
G. Whaples
Keyword(s):  
Rational Function ◽  
Number Field ◽  
Matrix Algebra ◽  
Function Fields ◽  
Simple Algebra ◽  
Noether Theorem ◽  
Full Matrix ◽  
Full Matrix Algebra ◽  
Rank One ◽  
Simple Algebras

The well-known Hasse-Brauer-Noether theorem states that a simple algebra with center a number field k splits over k (i.e., is a full matrix algebra) if and only if it splits over the completion of k at every rank one valuation of k. It is natural to ask whether this principle can be extended to a broader class of fields. In particular, we prove here the following extension.

Soluble-by-periodic skew linear groups

1984 ◽  
Vol 96 (3) ◽  
pp. 379-389 ◽  
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Finite Group ◽  
Positive Integer ◽  
Division Ring ◽  
Matrix Algebra ◽  
Locally Finite Group ◽  
Linear Groups ◽  
Locally Finite ◽  
Full Matrix ◽  
Full Matrix Algebra ◽  
Finite Image

Let D be a division ring with central subfield F, n a positive integer and G a subgroup of GL(n, D) such that the F-subalgebra F[G] generated by G is the full matrix algebra Dn×n. If G is soluble then Snider [9] proves that G is abelian by locally finite. He also shows that this locally finite image of G can be any locally finite group. Of course not every abelian by locally finite group is soluble. This suggests that Snider's conclusion should apply to some wider class of groups.

Group Gradings on Matrix Algebras

2002 ◽  
Vol 45 (4) ◽  
pp. 499-508 ◽  
Author(s):  
Yu. A. Bahturin ◽  
M. V. Zaicev
Keyword(s):  
Abelian Group ◽  
Tensor Product ◽  
Characteristic Zero ◽  
Matrix Algebra ◽  
Closed Field ◽  
Induction Procedure ◽  
Full Matrix ◽  
Full Matrix Algebra ◽  
Matrix Algebras ◽  
Group Gradings

AbstractLet Φ be an algebraically closed field of characteristic zero, G a finite, not necessarily abelian, group. Given a G-grading on the full matrix algebra A = Mn(Φ), we decompose A as the tensor product of graded subalgebras A = B ⊗ C, B ≅ Mp(Φ) being a graded division algebra, while the grading of C ≅ Mq(Φ) is determined by that of the vector space Φn. Now the grading of A is recovered from those of A and B using a canonical “induction” procedure.

scholarly journals The kS3-Module Algebra Structures on M3(k)

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 178
Author(s):  
Shiyin Zhao ◽  
Yin Wang ◽  
Xiaojuan Chen
Keyword(s):  
Symmetric Group ◽  
Matrix Algebra ◽  
Module Algebra ◽  
Full Matrix ◽  
Full Matrix Algebra

Let S 3 be the symmetric group on three elements. Let k be a field and M 3 ( k ) be the full matrix algebra of 3 × 3 -matrices over k. In this paper, the k S 3 -module algebra structures on M 3 ( k ) are described, and classified up to isomorphism.

scholarly journals Minor degenerations of the full matrix algebra over a field

2007 ◽  
Vol 59 (3) ◽  
pp. 763-795 ◽  
Author(s):  
Hisaaki FUJITA ◽  
Yosuke SAKAI ◽  
Daniel SIMSON
Keyword(s):  
Matrix Algebra ◽  
Full Matrix ◽  
Full Matrix Algebra ◽  
Algebra Over A Field

scholarly journals On diameter of the commuting graph of a full matrix algebra over a finite field

2016 ◽  
Vol 37 ◽  
pp. 36-45 ◽  
Author(s):  
David Dolžan ◽  
Damjana Kokol Bukovšek ◽  
Bojan Kuzma ◽  
Polona Oblak
Keyword(s):  
Finite Field ◽  
Matrix Algebra ◽  
Full Matrix ◽  
Full Matrix Algebra ◽  
Commuting Graph
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