Zariski Samuel Commutative Algebra !!BETTER!! Download Pdf
Zariski Samuel Commutative Algebra Download Pdf
A structure theorem for the automorphism of a locally connectedgroup is proved. The automorphism theorem is a tool for analyzingnon-automorohism of abstract groups avoiding the consideration overyoung automorphism groups and generalized simple groups. This theorem is shown to beequivalent to its restriction to the derived subgroup. An alternativeproof of the automorphism theorem based upon the use of normal subgroupsis presented. A geometric proof of the automorphism theorem is characterized. With the help of this theorem, a geometric criterion for the solvability of the conjugacy problem in an automorphism group is given.
We also apply the basic results on automorphisms of locally connected groupsand extend them to topological groups, which can be viewed ascontinuous locally connected groups with the discrete topology. Oneof the applications of the topological version of the automorphismtheorem is given to the study of automorphisms of unital Banach algebrasto be able to give a simple proof of Duad’s theorem on thesolvability of the conjugacy problem in prime dimension.
We show that every automorphism of a standard Leinert algebra is the product of an automorphism of thestandard part of the Leinert algebra and an inner automorphism of a homological extension algebra of the Leinert algebra. Leinert algebras were introduced by Leinert [5] and in this paper we prove a result on automorphisms ofthese algebras for the case of central simple Leinert algebras and we also generalize this result for an arbitrary finite-dimensional Leinert algebra. This provides a complete solution to Problem 1.1.2 posed by L.V.Drensky in [4].
We also discuss the question if every automorphism of an algebrasthe product of two automorphisms with disjoint ranges is the product of automorphisms with disjoint ranges. Based on this question we give several families of automorphisms ofassociative algebras, such as algebras of Cartan type, an algebrainvolving a free generator.
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