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Congruence classes and extensions of rings with an application to braces
Tomasz Brzezinski 
,
Bernard Rybolowicz
,
Bernard Rybolowicz
Communications in Contemporary Mathematics, Start page: 2050010
Swansea University Authors:
Tomasz Brzezinski , Bernard Rybolowicz
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DOI (Published version): 10.1142/s0219199720500108
Abstract
Two observations in support of the thesis that trusses are inherent in ring theory are made. First, it is shown that every equivalence class of a congruence relation on a ring or, equivalently, any element of the quotient of a ring R by an ideal I is a paragon in the truss T()T(R) associated to R. S...
| Published in: | Communications in Contemporary Mathematics |
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| ISSN: | 0219-1997 1793-6683 |
| Published: |
World Scientific Pub Co Pte Lt
2020
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa53070 |
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| Abstract: |
Two observations in support of the thesis that trusses are inherent in ring theory are made. First, it is shown that every equivalence class of a congruence relation on a ring or, equivalently, any element of the quotient of a ring R by an ideal I is a paragon in the truss T()T(R) associated to R. Second, an extension of a truss by a one-sided module is described. Even if the extended truss is associated to a ring, the resulting object is a truss, never a ring, unless the module is trivial. On the other hand, if the extended truss is associated to a brace, the resulting truss is also associated to a brace, irrespective of the module used. |
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| Keywords: |
Truss; heap; ring; brace; module |
| College: |
Faculty of Science and Engineering |
| Start Page: |
2050010 |