The relation between unique factorization, Krull-Schmidt Theorem and Jordan-Hölder Theorem was studied. Various examples of Jordan-Hölder type theorems existing in the mathematical literature were also discussed. The Jordan-Hölder Theorem and Schreier Theorem concern partial ordered set. The relation between these three contexts shows that some commutative monoid is free in all these three cases.
Descending chains of modules and Jordan-Holder theorem
DI RACCA, LUCA;FACCHINI, ALBERTO
2004
Abstract
The relation between unique factorization, Krull-Schmidt Theorem and Jordan-Hölder Theorem was studied. Various examples of Jordan-Hölder type theorems existing in the mathematical literature were also discussed. The Jordan-Hölder Theorem and Schreier Theorem concern partial ordered set. The relation between these three contexts shows that some commutative monoid is free in all these three cases.
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