The Zassenhaus lemma in star-regular categories. (English) Zbl 1428.18005
The Noether isomorphism theorems and the Zassenhaus Lemma are well known in group theory. O. Wyler [Arch. Math. 22, No. 1, 561–569 (1971; Zbl 0254.18004)] investigated a large class of pointed categories in which this theorems remain valid. W. Tholen [Relative Bildzerlegungen und algebraische Kategorien. Phd Thesis (1974)] gave a non-pointed version of this results in his doctoral dissertation. The authors of the paper under this review research this results in the framework of star-regular categories. They introduced some property \((\ast)\) and prove the isomorphism theorems. The Zassenhaus Lemma is established in a suitable categorical context. They get the new result in the category of cocommutative Hopf algebras also (the Zassenhaus Lemma).
Reviewer: Nikolay I. Kryuchkov (Ryazan)
MSC:
| 18A32 | Factorization systems, substructures, quotient structures, congruences, amalgams |
| 18A20 | Epimorphisms, monomorphisms, special classes of morphisms, null morphisms |
| 18A30 | Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) |
| 18C99 | Categories and theories |
| 16T05 | Hopf algebras and their applications |
Keywords:
factorisation systems; ideal of morphisms; normal category; star-regular category; ideal determined category; good theory of ideals; isomorphism theorems; Zassenhaus lemma; cocommutative Hopf algebraCitations:
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