Geodesic
The Rings Which Can Be Recovered by Means of the Difference
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 1, pp. 49-55 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 06E20, 06E30, 13A99, 13B25
Keywords: Boolean ring; commutative ring; lattice-like structure; difference 
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Chajda, Ivan; Švrček, Filip. The Rings Which Can Be Recovered by Means of the Difference. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 1, pp. 49-55. http://geodesic.mathdoc.fr/item/AUPO_2013_52_1_a3/