| Title:
|
$\Sigma$-isomorphic algebraic structures (English) |
| Author:
|
Chajda, Ivan |
| Author:
|
Emanovský, Petr |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
120 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
71-81 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For an algebraic structure $\A=(A,F,R)$ or type $\t$ and a set $\Sigma$ of open formulas of the first order language $L(\t)$ we introduce the concept of $\Sigma$-closed subsets of $\A$. The set $\C_\Sigma(\A)$ of all $\Sigma$-closed subsets forms a complete lattice. Algebraic structures $\A$, $\B$ of type $\t$ are called $\Sigma$-isomorphic if $\C_\Sigma(\A)\cong\C_\Sigma(\B)$. Examples of such $\Sigma$-closed subsets are e.g. subalgebras of an algebra, ideals of a ring, ideals of a lattice, convex subsets of an ordered or quasiordered set etc. We study $\Sigma$-isomorphic algebraic structures in dependence on the properties of $\Sigma$. (English) |
| Keyword:
|
closure system |
| Keyword:
|
isomorphism |
| Keyword:
|
lattice of $\Sigma$-closed subsets |
| Keyword:
|
subalgebras |
| Keyword:
|
ideals |
| Keyword:
|
algebraic structure |
| Keyword:
|
$\Sigma$-closed subset |
| Keyword:
|
$\Sigma$-isomorphic structures |
| MSC:
|
03C05 |
| MSC:
|
04A05 |
| MSC:
|
06B10 |
| MSC:
|
08A05 |
| idZBL:
|
Zbl 0833.08001 |
| idMR:
|
MR1336947 |
| DOI:
|
10.21136/MB.1995.125890 |
| . |
| Date available:
|
2009-09-24T21:09:06Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125890 |
| . |
| 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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| Reference:
|
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| . |
