Lifting multiplicative lattices to ideal sytems
Tiberiu Dumitrescu, Mihai Epure, Alexandru Gica
Abstract
We present a mechanism which lifts a multiplicative lattice to a (weak) ideal system on some monoid.
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Lifting multiplicative lattices to ideal sytems
Authors
Abstract
We present a mechanism which lifts a multiplicative lattice to a (weak) ideal system on some monoid.
Paper Structure (5 theorems, 20 equations)
This paper contains 5 theorems, 20 equations.
Key Result
Theorem 2
Let $H$ be a monoid and $r$ a weak ideal system on $H$. Then the set of all r-ideals of $H$ is a lattice w.r.t. following operations multiplication: $(X,Y)\mapsto (XY)_r$ for all $X,Y \in I_r(H)$, join: $\bigvee \Gamma := (\bigcup \Gamma)_r$ for all $\Gamma \subseteq I_r(H)$, meet: $\bigwedge \Gamma := \bigcap \Gamma$ for all $\Gamma \subseteq I_r(H)$, where $\bigcup
Theorems & Definitions (16)
- Definition 1
- Theorem 2
- Definition 3
- Theorem 4
- proof
- Corollary 5
- proof
- Example 6
- Proposition 7
- proof
- ...and 6 more