| Title:
|
Directoids with an antitone involution (English) |
| Author:
|
Chajda, I. |
| Author:
|
Kolařík, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
555-569 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate $\sqcap$-directoids which are bounded and equipped by a unary operation which is an antitone involution. Hence, a new operation $\sqcup$ can be introduced via De Morgan laws. Basic properties of these algebras are established. On every such an algebra a ring-like structure can be derived whose axioms are similar to that of a generalized boolean quasiring. We introduce a concept of symmetrical difference and prove its basic properties. Finally, we study conditions of direct decomposability of directoids with an antitone involution. (English) |
| Keyword:
|
directoid |
| Keyword:
|
antitone involution |
| Keyword:
|
D-quasiring |
| Keyword:
|
symmetrical difference |
| Keyword:
|
direct decomposition |
| MSC:
|
06A06 |
| MSC:
|
06A12 |
| MSC:
|
06E20 |
| MSC:
|
16Y99 |
| idZBL:
|
Zbl 1199.06012 |
| idMR:
|
MR2375158 |
| . |
| Date available:
|
2009-05-05T17:04:42Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119680 |
| . |
| 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:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| . |
