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1
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On derivations of quantales

100%
Xiao Q., Liu W.
Open Mathematics
|
2016
|
tom 14
|
nr 1
338-346
EN
A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation.
2
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A note on Stone join-semilattices

76%
Nimbhorkar S., Rahemani A.
Open Mathematics
|
2011
|
tom 9
|
nr 4
929-933
EN
Characterizations for a pseudocomplemented modular join-semilattice with 0 and 1 and its ideal lattice to be a Stone lattice are given.
3
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Scott convergence and fuzzy Scott topology onL-posets

76%
Liu H., Chen L.
Open Mathematics
|
2017
|
tom 15
|
nr 1
815-827
EN
We firstly generalize the fuzzy way-below relation on an L-poset, and consider its continuity by means of this relation. After that, we introduce a kind of stratified L-generalized convergence structure on an L-poset. In terms of that, L-fuzzy Scott topology and fuzzy Scott topology are considered, and the properties of fuzzy Scott topology are discussed in detail. At last, we investigate the Scott convergence of stratified L-filters on an L-poset, and show that an L-poset is continuous if and only if the Scott convergence on it coincides with the convergence with respect to the corresponding topological space.
4
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Ideals which generalize (v 0)

76%
Kalemba P., Plewik S.
Open Mathematics
|
2010
|
tom 8
|
nr 6
1016-1025
EN
Countable products of finite discrete spaces with more than one point and ideals generated by Marczewski-Burstin bases (assigned to trimmed trees) are examined, using machinery of base tree in the sense of B. Balcar and P. Simon. Applying Kulpa-Szymanski Theorem, we prove that the covering number equals to the additivity or the additivity plus for each of the ideals considered.
5
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Ideals in distributive posets

64%
Batueva C., Semenova M.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1380-1388
EN
We prove that any ideal in a distributive (relative to a certain completion) poset is an intersection of prime ideals. Besides that, we give a characterization of n-normal meet semilattices with zero, thus generalizing a known result for lattices with zero.
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