| Title:
|
The Rings Which Can Be Recovered by Means of the Difference (English) |
| Author:
|
Chajda, Ivan |
| Author:
|
Švrček, Filip |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
49-55 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Boolean ring |
| Keyword:
|
commutative ring |
| Keyword:
|
lattice-like structure |
| Keyword:
|
difference |
| MSC:
|
06E20 |
| MSC:
|
06E30 |
| MSC:
|
13A99 |
| MSC:
|
13B25 |
| idZBL:
|
Zbl 06285753 |
| idMR:
|
MR3202748 |
| . |
| Date available:
|
2013-08-02T07:54:35Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143390 |
| . |
| Reference:
|
[1] Birkhoff, G.: Lattice Theory. 3rd edition, AMS Colloq. Publ. 25, Providence, RI, 1979. Zbl 0505.06001, MR 0598630 |
| Reference:
|
[2] Chajda, I.: Pseudosemirings induced by ortholattices. Czech. Math. J. 46 (2008), 405–411. MR 1408295 |
| Reference:
|
[3] Chajda, I., Eigenthaler, G.: A note on orthopseudorings and Boolean quasirings. Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 207 (1998), 83–94. Zbl 1040.06003, MR 1749914 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[9] Dorninger, D., Länger, H., Ma̧cyński, M.: Lattice properties of ring-like quantum logics. Intern. J. Theor. Phys. 39 (2000), 1015–1026. MR 1779170, 10.1023/A:1003646323230 |
| Reference:
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| Reference:
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| Reference:
|
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| . |
