Classical Ideal Semigroups
| Autor: | Bruno Bosbach |
|---|---|
| Rok vydání: | 2000 |
| Předmět: |
Discrete mathematics
Overline Mathematics::Complex Variables Applied Mathematics Image (category theory) High Energy Physics::Phenomenology Prime (order theory) symbols.namesake Mathematics (miscellaneous) Product (mathematics) symbols Ideal (ring theory) Noether's theorem Algebraic number Commutative property Mathematics |
| Zdroj: | Results in Mathematics. 37:36-46 |
| ISSN: | 1420-9012 0378-6218 |
| DOI: | 10.1007/bf03322510 |
| Popis: | Based on the notion of an algebraic m-lattice Open image in new window an abstract commutative ideal theory for commutative monoids is developed. Open image in new window is called classical iff it is modular and if for each prime p the mapping \(a\mapsto \overline a\:=p+a\) satisfies \(\overline a \cdot \overline x =\overline a \cdot \overline \eta \Rightarrow \overline a=\overline p\ {\rm V}\ \overline x=\overline \eta \). Let Open image in new window be classical, then any ideal is a product of prime ideals iff Open image in new window satisfies the Noether property together with (M) \(a \supseteq b\Longrightarrow a \mid b\) or iff Open image in new window satisfies the Noether property together with the Sono property, that is \(m \supseteq x\supseteq m^2 \Longrightarrow m=x\ {\rm V}\ x=m^2\) (for maximal m). |
| Databáze: | OpenAIRE |
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