Multiplicatively Idempotent Semirings
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| 024 | 7 | 0 | |a 10.1007/s10958-015-2340-6 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2340-6 | ||
| 245 | 0 | 0 | |a Multiplicatively Idempotent Semirings |h [Elektronische Daten] |c [E. Vechtomov, A. Petrov] |
| 520 | 3 | |a The article is devoted to the investigation of semirings with idempotent multiplication. General structure theorems for such semirings are proved. We focus on the study of the class M $$ \mathfrak{M} $$ of all commutative multiplicatively idempotent semirings. We obtain necessary conditions under which semirings from M $$ \mathfrak{M} $$ are subdirectly irreducible. We consider some properties of the variety M $$ \mathfrak{M} $$ . In particular, we show that M $$ \mathfrak{M} $$ is generated by two of its subvarieties, defined by the identities 3x = x and 3x = 2x. We explore the variety N $$ \mathfrak{N} $$ generated by two-element commutative multiplicatively idempotent semirings. It is proved that the lattice of all subvarieties of N $$ \mathfrak{N} $$ is a 16-element Boolean lattice. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 700 | 1 | |a Vechtomov |D E. |u Vyatka State University of Humanities, Vyatka, Russia |4 aut | |
| 700 | 1 | |a Petrov |D A. |u Vyatka State University of Humanities, Vyatka, Russia |4 aut | |
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 206/6(2015-05-01), 634-653 |x 1072-3374 |q 206:6<634 |1 2015 |2 206 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2340-6 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10958-015-2340-6 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Vechtomov |D E. |u Vyatka State University of Humanities, Vyatka, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Petrov |D A. |u Vyatka State University of Humanities, Vyatka, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 206/6(2015-05-01), 634-653 |x 1072-3374 |q 206:6<634 |1 2015 |2 206 |o 10958 | ||