The Rings Which Can Be Recovered by Means of the Difference

@article{Chajda2013,
abstract = {It is well known that to every Boolean ring $\mathcal \{R\}$ can be assigned a Boolean algebra $\mathcal \{B\}$ whose operations are term operations of $\mathcal \{R\}$. Then a symmetric difference of $\mathcal \{B\}$ together with the meet operation recover the original ring operations of $\mathcal \{R\}$. The aim of this paper is to show for what a ring $\mathcal \{R\}$ a similar construction is possible. Of course, we do not construct a Boolean algebra but only so-called lattice-like structure which was introduced and treated by the authors in a previous paper. In particular, we reached interesting results if the characteristic of the ring $\mathcal \{R\}$ is either an odd natural number or a power of 2.},
author = {Chajda, Ivan, Švrček, Filip},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Boolean ring; commutative ring; lattice-like structure; difference; Boolean rings; commutative rings; ring operations; lattice-like structures; symmetric difference},
language = {eng},
number = {1},
pages = {49-55},
publisher = {Palacký University Olomouc},
title = {The Rings Which Can Be Recovered by Means of the Difference},
url = {http://eudml.org/doc/260732},
volume = {52},
year = {2013},
}

TY - JOUR
AU - Chajda, Ivan
AU - Švrček, Filip
TI - The Rings Which Can Be Recovered by Means of the Difference
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2013
PB - Palacký University Olomouc
VL - 52
IS - 1
SP - 49
EP - 55
AB - It is well known that to every Boolean ring $\mathcal {R}$ can be assigned a Boolean algebra $\mathcal {B}$ whose operations are term operations of $\mathcal {R}$. Then a symmetric difference of $\mathcal {B}$ together with the meet operation recover the original ring operations of $\mathcal {R}$. The aim of this paper is to show for what a ring $\mathcal {R}$ a similar construction is possible. Of course, we do not construct a Boolean algebra but only so-called lattice-like structure which was introduced and treated by the authors in a previous paper. In particular, we reached interesting results if the characteristic of the ring $\mathcal {R}$ is either an odd natural number or a power of 2.
LA - eng
KW - Boolean ring; commutative ring; lattice-like structure; difference; Boolean rings; commutative rings; ring operations; lattice-like structures; symmetric difference
UR - http://eudml.org/doc/260732
ER -