| Title:
|
Some properties of state filters in state residuated lattices (English) |
| Author:
|
Kondo, Michiro |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
146 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
375-395 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider properties of state filters of state residuated lattices and prove that for every state filter $F$ of a state residuated lattice $X$: \begin {itemize} \item [(1)] $F$ is obstinate $\Leftrightarrow $ $L/F \cong \{0,1\}$; \item [(2)] $F$ is primary $\Leftrightarrow $ $L/F$ is a state local residuated lattice; \end {itemize} and that every g-state residuated lattice $X$ is a subdirect product of $\{X/P_{\lambda } \}$, where $P_{\lambda }$ is a prime state filter of $X$. \endgraf Moreover, we show that the quotient MTL-algebra $X/P$ of a state residuated lattice $X$ by a state prime filter $P$ is not always totally ordered, although the quotient MTL-algebra by a prime filter is totally ordered. (English) |
| Keyword:
|
obstinate state filter |
| Keyword:
|
prime state filter |
| Keyword:
|
Boolean state filter |
| Keyword:
|
primary state filter |
| Keyword:
|
state filter |
| Keyword:
|
residuated lattice |
| Keyword:
|
local residuated lattice |
| MSC:
|
03B47 |
| MSC:
|
06B10 |
| idZBL:
|
Zbl 07442508 |
| idMR:
|
MR4336545 |
| DOI:
|
10.21136/MB.2020.0040-19 |
| . |
| Date available:
|
2021-11-08T16:18:04Z |
| Last updated:
|
2021-12-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149254 |
| . |
| Reference:
|
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