Baer-Kaplansky classes of vector spaces and modules determined by numerical invariants

Gabriella D’Este; Derya Keskin Tütüncü; Rachid Tribak

doi:10.1080/00927872.2022.2125981

Baer-Kaplansky classes of vector spaces and modules determined by numerical invariants

Gabriella D’Este
, Derya Keskin Tütüncü
, Rachid Tribak

Division of Algebra and Number Theory

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

1 Citation (Scopus)

Abstract

We show that reasonably large classes (Formula presented.) of vector spaces, modules over noncommutative algebras and abelian groups are Baer-Kaplansky classes with additional properties. Indeed, modules in (Formula presented.) such that their endomorphism rings are isomorphic vector spaces, or modules such that their endomorphism rings are isomorphic vector spaces with the same number of primitive idempotents may be actually isomorphic.

Original language	English
Pages (from-to)	1089-1104
Number of pages	16
Journal	Communications in Algebra
Volume	51
Issue number	3
DOIs	https://doi.org/10.1080/00927872.2022.2125981
Publication status	Published - 2023

Keywords

Abelian groups
Baer-Kaplansky classes
Baer-Kaplansky theorem
quivers and their representations

Access to Document

10.1080/00927872.2022.2125981

Cite this

@article{595923b2c1684d80b6115f9af0f369ab,

title = "Baer-Kaplansky classes of vector spaces and modules determined by numerical invariants",

abstract = "We show that reasonably large classes (Formula presented.) of vector spaces, modules over noncommutative algebras and abelian groups are Baer-Kaplansky classes with additional properties. Indeed, modules in (Formula presented.) such that their endomorphism rings are isomorphic vector spaces, or modules such that their endomorphism rings are isomorphic vector spaces with the same number of primitive idempotents may be actually isomorphic.",

keywords = "Abelian groups, Baer-Kaplansky classes, Baer-Kaplansky theorem, quivers and their representations",

author = "Gabriella D{\textquoteright}Este and T{\"u}t{\"u}nc{\"u}, \{Derya Keskin\} and Rachid Tribak",

note = "Publisher Copyright: {\textcopyright} 2022 Taylor \& Francis Group, LLC.",

year = "2023",

doi = "10.1080/00927872.2022.2125981",

language = "English",

volume = "51",

pages = "1089--1104",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

number = "3",

}

TY - JOUR

T1 - Baer-Kaplansky classes of vector spaces and modules determined by numerical invariants

AU - D’Este, Gabriella

AU - Tütüncü, Derya Keskin

AU - Tribak, Rachid

PY - 2023

Y1 - 2023

N2 - We show that reasonably large classes (Formula presented.) of vector spaces, modules over noncommutative algebras and abelian groups are Baer-Kaplansky classes with additional properties. Indeed, modules in (Formula presented.) such that their endomorphism rings are isomorphic vector spaces, or modules such that their endomorphism rings are isomorphic vector spaces with the same number of primitive idempotents may be actually isomorphic.

AB - We show that reasonably large classes (Formula presented.) of vector spaces, modules over noncommutative algebras and abelian groups are Baer-Kaplansky classes with additional properties. Indeed, modules in (Formula presented.) such that their endomorphism rings are isomorphic vector spaces, or modules such that their endomorphism rings are isomorphic vector spaces with the same number of primitive idempotents may be actually isomorphic.

KW - Abelian groups

KW - Baer-Kaplansky classes

KW - Baer-Kaplansky theorem

KW - quivers and their representations

UR - https://www.scopus.com/pages/publications/85141047627

U2 - 10.1080/00927872.2022.2125981

DO - 10.1080/00927872.2022.2125981

M3 - Article

AN - SCOPUS:85141047627

SN - 0092-7872

VL - 51

SP - 1089

EP - 1104

JO - Communications in Algebra

JF - Communications in Algebra

IS - 3

ER -

Baer-Kaplansky classes of vector spaces and modules determined by numerical invariants

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this