Geodesic
Spectra of locally matrix algebras
Algebra and discrete mathematics, Tome 31 (2021) no. 1, pp. 17-36.

Voir la notice de l'article provenant de la source Math-Net.Ru

We describe spectra of associative (not necessarily unital and not necessarily countable-dimensional) locally matrix algebras. We determine all possible spectra of locally matrix algebras and give a new proof of Dixmier–Baranov Theorem. As an application of our description of spectra, we determine embeddings of locally matrix algebras.
Keywords: locally matrix algebra, Steinitz number, spectrum, embedding. 
@article{ADM_2021_31_1_a1,
     author = {O. Bezushchak},
     title = {Spectra of locally matrix algebras},
     journal = {Algebra and discrete mathematics},
     pages = {17--36},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a1/}
}
TY  - JOUR
AU  - O. Bezushchak
TI  - Spectra of locally matrix algebras
JO  - Algebra and discrete mathematics
PY  - 2021
SP  - 17
EP  - 36
VL  - 31
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a1/
LA  - en
ID  - ADM_2021_31_1_a1
ER  - 
%0 Journal Article
%A O. Bezushchak
%T Spectra of locally matrix algebras
%J Algebra and discrete mathematics
%D 2021
%P 17-36
%V 31
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a1/
%G en
%F ADM_2021_31_1_a1
O. Bezushchak. Spectra of locally matrix algebras. Algebra and discrete mathematics, Tome 31 (2021) no. 1, pp. 17-36. http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a1/

[1] A. A. Baranov, “Classification of the direct limits of involution simple associative algebras and the corresponding dimension groups”, Journal of Algebra, 381 (2013), 73–95 | DOI | MR | Zbl

[2] O. Bezushchak and B. Oliynyk, “Unital locally matrix algebras and Steinitz numbers”, J. Algebra Appl., 19:9 (2020) | DOI | MR

[3] O. Bezushchak and B. Oliynyk, “Primary decompositions of unital locally matrix algebras”, Bull. Math. Sci., 10:1 (2020) | DOI | MR | Zbl

[4] O. Bezushchak and B. Oliynyk, “Morita equivalent unital locally matrix algebras”, Algebra Discrete Math., 29:2 (2020), 173–179 | DOI | MR | Zbl

[5] J. Dixmier, “On some $C^{*}$-algebras considered by Glimm”, J. Funct. Anal., 1 (1967), 182–203 | DOI | MR | Zbl

[6] Yu. A. Drozd, V. V. Kirichenko, Finite dimensional algebras, Springer-Verlag, Berlin–Heidelberg–New York, 1994 | MR | Zbl

[7] J. G. Glimm, “On a certain class of operator algebras”, Trans. Amer. Math. Soc., 95:2 (1960), 318–340 | DOI | MR | Zbl

[8] N. Jacobson, Structure of rings, Colloquium Publications, 37, 1956 | DOI | MR | Zbl

[9] V. M. Kurochkin, “On the theory of locally simple and locally normal algebras”, Mat. Sb., N.S., 22(64):3 (1948), 443–454 | MR | Zbl

[10] A. Kurosh, “Direct decompositions of simple rings”, Rec. Math. [Mat. Sbornik] N.S., 11(53):3 (1942), 245–264 | MR | Zbl

[11] E. Steinitz, “Algebraische Theorie der Körper”, Journal für die reine und angewandte Mathematik, 137 (1910), 167–309 | DOI | MR | Zbl