Mal'tsev--Neumann products of semi-simple classes of rings

Barry James Gardner

Commentationes Mathematicae Universitatis Carolinae (2022)

  • Volume: 62 63, Issue: 4, page 415-421
  • ISSN: 0010-2628

Abstract

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Malt’tsev–Neumann products of semi-simple classes of associative rings are studied and some conditions which ensure that such a product is again a semi-simple class are obtained. It is shown that both products, 𝒮 1 ∘ 𝒮 2 and 𝒮 2 ∘ 𝒮 1 of semi-simple classes 𝒮 1 and 𝒮 2 are semi-simple classes if and only if they are equal.

How to cite

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Gardner, Barry James. "Mal'tsev--Neumann products of semi-simple classes of rings." Commentationes Mathematicae Universitatis Carolinae 62 63.4 (2022): 415-421. <http://eudml.org/doc/299046>.

@article{Gardner2022,
abstract = {Malt’tsev–Neumann products of semi-simple classes of associative rings are studied and some conditions which ensure that such a product is again a semi-simple class are obtained. It is shown that both products, $\mathcal \{S\}_\{1\}\circ \mathcal \{S\}_\{2\}$ and $\mathcal \{S\}_\{2\}\circ \mathcal \{S\}_\{1\}$ of semi-simple classes $\mathcal \{S\}_\{1\}$ and $\mathcal \{S\}_\{2\}$ are semi-simple classes if and only if they are equal.},
author = {Gardner, Barry James},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {radical class; semi-simple class; Mal'tsev--Neumann product},
language = {eng},
number = {4},
pages = {415-421},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Mal'tsev--Neumann products of semi-simple classes of rings},
url = {http://eudml.org/doc/299046},
volume = {62 63},
year = {2022},
}

TY - JOUR
AU - Gardner, Barry James
TI - Mal'tsev--Neumann products of semi-simple classes of rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2022
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62 63
IS - 4
SP - 415
EP - 421
AB - Malt’tsev–Neumann products of semi-simple classes of associative rings are studied and some conditions which ensure that such a product is again a semi-simple class are obtained. It is shown that both products, $\mathcal {S}_{1}\circ \mathcal {S}_{2}$ and $\mathcal {S}_{2}\circ \mathcal {S}_{1}$ of semi-simple classes $\mathcal {S}_{1}$ and $\mathcal {S}_{2}$ are semi-simple classes if and only if they are equal.
LA - eng
KW - radical class; semi-simple class; Mal'tsev--Neumann product
UR - http://eudml.org/doc/299046
ER -

References

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  1. Fuchs L., Abelian Groups, Springer Monographs in Mathematics, Springer, Cham, 2015. Zbl1265.06054MR3467030
  2. Gardner B. J., 10.24330/ieja.440117, Int. Electron. J. Algebra 24 (2018), 1–11. MR3828091DOI10.24330/ieja.440117
  3. Gardner B. J., Wiegandt R., Radical Theory of Rings, Monographs and Textbooks in Pure and Applied Mathematics, 261, Marcel Dekker, New York, 2004. MR2015465
  4. Mal'tsev A. I., Ob umnozhenii klassov algebraicheskikh sistem, Sibirskii Mat. Zh. 8 (1967), 346–365 (Russian). MR0213276
  5. Neumann H., Varieties of Groups, Springer, New York, 1967. Zbl0251.20001MR0215899
  6. Penza T., Romanowska A. B., Mal'tsev products of varieties, I., Algebra Universalis 82 (2021), no. 2, Paper No. 33, 19 pages. MR4251619
  7. Snider R. L., 10.1307/mmj/1029000265, Michigan Math. J. 16 (1969), 225–226. MR0248177DOI10.1307/mmj/1029000265

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