Frobenius type theorems in the noncommutative case

Alexander Guterman

doi:10.1080/03081080108818676

Frobenius type theorems in the noncommutative case

Alexander Guterman

Lomonosov Moscow State University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The classification of semilinear transformations preserving the determinant over a noncommutative local ring is given. For local Ore domains we obtain a classification of Adjamagbo determinant preservers. The developed technique allows us to classify Dieudonné determinant preservers for division rings which may be infinite dimensional over the center.

Original language	English
Pages (from-to)	293-311
Number of pages	19
Journal	Linear and Multilinear Algebra
Volume	48
Issue number	4
DOIs	https://doi.org/10.1080/03081080108818676
State	Published - 2001
Externally published	Yes

Bibliographical note

Funding Information:
*This work is partially supported by RFBR Grants NN 96-15-96050, 99-01-00382. +,-mail: [email protected]

Keywords

Dieudonné determinant
Linear preservers
Local rings

Access to Document

10.1080/03081080108818676

Cite this

@article{1c68d5db224540648547c7471f6ea68f,

title = "Frobenius type theorems in the noncommutative case",

abstract = "The classification of semilinear transformations preserving the determinant over a noncommutative local ring is given. For local Ore domains we obtain a classification of Adjamagbo determinant preservers. The developed technique allows us to classify Dieudonn{\'e} determinant preservers for division rings which may be infinite dimensional over the center.",

keywords = "Dieudonn{\'e} determinant, Linear preservers, Local rings",

author = "Alexander Guterman",

note = "Funding Information: *This work is partially supported by RFBR Grants NN 96-15-96050, 99-01-00382. +,-mail: [email protected]",

year = "2001",

doi = "10.1080/03081080108818676",

language = "אנגלית",

volume = "48",

pages = "293--311",

journal = "Linear and Multilinear Algebra",

issn = "0308-1087",

publisher = "Taylor and Francis Ltd.",

number = "4",

}

TY - JOUR

T1 - Frobenius type theorems in the noncommutative case

AU - Guterman, Alexander

N1 - Funding Information: *This work is partially supported by RFBR Grants NN 96-15-96050, 99-01-00382. +,-mail: [email protected]

PY - 2001

Y1 - 2001

N2 - The classification of semilinear transformations preserving the determinant over a noncommutative local ring is given. For local Ore domains we obtain a classification of Adjamagbo determinant preservers. The developed technique allows us to classify Dieudonné determinant preservers for division rings which may be infinite dimensional over the center.

AB - The classification of semilinear transformations preserving the determinant over a noncommutative local ring is given. For local Ore domains we obtain a classification of Adjamagbo determinant preservers. The developed technique allows us to classify Dieudonné determinant preservers for division rings which may be infinite dimensional over the center.

KW - Dieudonné determinant

KW - Linear preservers

KW - Local rings

UR - https://www.scopus.com/pages/publications/0012348075

U2 - 10.1080/03081080108818676

DO - 10.1080/03081080108818676

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0012348075

SN - 0308-1087

VL - 48

SP - 293

EP - 311

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 4

ER -

Frobenius type theorems in the noncommutative case

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this