The Rings Which Can Be Recovered by Means of the Difference

Chajda, Ivan, and Švrček, Filip. "The Rings Which Can Be Recovered by Means of the Difference." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 52.1 (2013): 49-55. <http://eudml.org/doc/260732>.

@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 -