| Title:
|
Congruences and ideals in ternary rings (English) |
| Author:
|
Chajda, Ivan |
| Author:
|
Halaš, Radomír |
| Author:
|
Machala, František |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
163-172 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A ternary ring is an algebraic structure ${\mathcal R}=(R;t,0,1)$ of type $(3,0,0)$ satisfying the identities $t(0,x,y)=y=t(x,0,y)$ and $t(1,x,0)=x=(x,1,0)$ where, moreover, for any $a$, $b$, $c\in R$ there exists a unique $d\in R$ with $t(a,b,d)=c$. A congruence $\theta $ on ${\mathcal R}$ is called normal if ${\mathcal R}/\theta $ is a ternary ring again. We describe basic properties of the lattice of all normal congruences on ${\mathcal R}$ and establish connections between ideals (introduced earlier by the third author) and congruence kernels. (English) |
| Keyword:
|
ternary ring |
| Keyword:
|
ideal |
| Keyword:
|
congruence |
| Keyword:
|
normal congruence |
| Keyword:
|
congruence kernel |
| MSC:
|
08A05 |
| MSC:
|
08A30 |
| MSC:
|
13A15 |
| MSC:
|
17A40 |
| MSC:
|
20N10 |
| idZBL:
|
Zbl 0934.17001 |
| idMR:
|
MR1435614 |
| . |
| Date available:
|
2009-09-24T10:03:41Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127347 |
| . |
| Reference:
|
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| Reference:
|
[2] R. Bělohlávek, I. Chajda: Congruences and ideals in semiloops.Acta Sci. Math. (Szeged) 59 (1994), 43–47. |
| Reference:
|
[3] I. Chajda, R. Halaš: Ideals in bi-ternary rings.Discussione Math. Algebra and Stochastic Methods 15 (1995), 11–21. |
| Reference:
|
[4] H.P. Gumm, A. Ursini: Ideals in universal algebra.Algebra Univ. 19 (1984), 45–54. 10.1007/BF01191491 |
| Reference:
|
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| Reference:
|
[6] B. Jónsson: On the representation of lattices.Math. Scand. 1 (1953), 193–206. 10.7146/math.scand.a-10377 |
| Reference:
|
[7] F. Machala: Erweiterte lokale Ternärringe.Czech. Math. J. 27 (1977), 560–572. Zbl 0391.17003 |
| Reference:
|
[8] F. Machala: Koordinatisation projectiver Ebenen mit Homomorphismus.Czech. Math. J. 27 (1977), 573–590. |
| Reference:
|
[9] F. Machala: Koordinatisation affiner Ebenen mit Homomorphismus.Math. Slovaca 27 (1977), 181–193. Zbl 0359.50017 |
| Reference:
|
[10] G. Pickert: ARRAY(0x9fa9250).Heidelberg, New York, 1975, pp. . |
| Reference:
|
[11] A. Ursini: Sulle varietá di algebra con una buona teoria degli ideali.Bull. U.M.I. 6 (1972), no. 4, 90–95. |
| . |
