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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.