Keywords: $*$-regular ring; representable; unit-regular
@article{10_5817_AM2020_1_43,
author = {Herrmann, Christian},
title = {Unit-regularity and representability for semiartinian $*$-regular rings},
journal = {Archivum mathematicum},
pages = {43--47},
year = {2020},
volume = {56},
number = {1},
doi = {10.5817/AM2020-1-43},
mrnumber = {4075887},
zbl = {07177879},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2020-1-43/}
}
TY - JOUR AU - Herrmann, Christian TI - Unit-regularity and representability for semiartinian $*$-regular rings JO - Archivum mathematicum PY - 2020 SP - 43 EP - 47 VL - 56 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.5817/AM2020-1-43/ DO - 10.5817/AM2020-1-43 LA - en ID - 10_5817_AM2020_1_43 ER -
Herrmann, Christian. Unit-regularity and representability for semiartinian $*$-regular rings. Archivum mathematicum, Tome 56 (2020) no. 1, pp. 43-47. doi: 10.5817/AM2020-1-43
[1] Baccella, G., Spinosa, L.: $K_0$ of semiartinian von Neumann regular rings. Direct finiteness versusunit-regularity. Algebr. Represent. Theory 20 (2017), 1189–1213. | DOI | MR
[2] Berberian, S.K.: Baer *-rings. Springer, Grundlehren 195, Berlin, 1972. | MR
[3] Goodearl, K.R.: Von Neumann Regular Rings. 2nd ed., Krieger, Malabar, 1991. | MR
[4] Gross, H.: Quadratic Forms in Infinite Dimensional Vector spaces. Birkhäuser, Basel, 1979. | MR
[5] Handelman, D.: Finite Rickart C$^*$-algebras and their properties. Adv. in Math. Suppl. Stud., vol. 4, Academic Press, New York-London, Studies in analysis ed., 1979, pp. 171–196. | MR
[6] Herrmann, C.: Varieties of $*$-regular rings. | arXiv
[7] Herrmann, C.: On the equational theory of projection lattices of finitevon Neumann factors. J. Symbolic Logic 75 (3) (2010), 1102–1110. | DOI | MR
[8] Herrmann, C.: Direct finiteness of representable regular $*$-rings. Algebra Universalis 80 (1) (2019), 5 pp., | arXiv | MR
[9] Herrmann, C., Semenova, M.V.: Rings of quotients of finite AW$^*$-algebras. Representation and algebraic approximation. Algebra Logika 53 (4) (2014), 466–504, 550–551, (Russian), translation inAlgebra Logic 53 (2014), no. 4, 298–322. | DOI | MR
[10] Herrmann, C., Semenova, M.V.: Linear representations of regular rings and complemented modular lattices with involution. Acta Sci. Math. (Szeged) 82 (3–4) (2016), 395–442. | DOI | MR
[11] Jacobson, N.: Structure of Rings. AMS Col. Publ. XXXVII, Amer. Math. Soc., Providence, RI, 1956. | MR | Zbl
[12] Micol, F.: On representability of $\ast $-regular rings and modular ortholattices. Ph.D. thesis, TU Darmstadt, January 2003, http://elib.tu-darmstadt.de/diss/000303/diss.pdf
[13] Wehrung, F.: A uniform refinement property for congruence lattices. Proc. Amer. Math. Soc. 127 (1999), 363–370. | DOI | MR | Zbl
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