Congruences and ideals in ternary rings

Ivan Chajda; Radomír Halaš; František Machala

Czechoslovak Mathematical Journal (1997)

  • Volume: 47, Issue: 1, page 163-172
  • ISSN: 0011-4642

Abstract

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A ternary ring is an algebraic structure 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 ∈ R there exists a unique d ∈ R with t ( a , b , d ) = c . A congruence θ on ℛ is called normal if ℛ / θ is a ternary ring again. We describe basic properties of the lattice of all normal congruences on ℛ and establish connections between ideals (introduced earlier by the third author) and congruence kernels.

How to cite

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Chajda, Ivan, Halaš, Radomír, and Machala, František. "Congruences and ideals in ternary rings." Czechoslovak Mathematical Journal 47.1 (1997): 163-172. <http://eudml.org/doc/30355>.

@article{Chajda1997,
abstract = {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.},
author = {Chajda, Ivan, Halaš, Radomír, Machala, František},
journal = {Czechoslovak Mathematical Journal},
keywords = {ternary ring; ideal; congruence; normal congruence; congruence kernel; ternary ring; ideal; congruence},
language = {eng},
number = {1},
pages = {163-172},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Congruences and ideals in ternary rings},
url = {http://eudml.org/doc/30355},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Chajda, Ivan
AU - Halaš, Radomír
AU - Machala, František
TI - Congruences and ideals in ternary rings
JO - Czechoslovak Mathematical Journal
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 1
SP - 163
EP - 172
AB - 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.
LA - eng
KW - ternary ring; ideal; congruence; normal congruence; congruence kernel; ternary ring; ideal; congruence
UR - http://eudml.org/doc/30355
ER -

References

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  10. ARRAY(0x9fa9250), Heidelberg, New York, 1975, pp. . (1975) 
  11. Sulle varietá di algebra con una buona teoria degli ideali, Bull. U.M.I. 6 (1972), no. 4, 90–95. (1972) 

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