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On subrings of amalgamated free products of rings

James Renshaw (1999)

Colloquium Mathematicae

The aim of this paper is to develop the homological machinery needed to study amalgams of subrings. We follow Cohn [1] and describe an amalgam of subrings in terms of reduced iterated tensor products of the rings forming the amalgam and prove a result on embeddability of amalgamated free products. Finally we characterise the commutative perfect amalgamation bases.

On the binary system of factors of formal matrix rings

Weining Chen, Guixin Deng, Huadong Su (2020)

Czechoslovak Mathematical Journal

We investigate the formal matrix ring over R defined by a certain system of factors. We give a method for constructing formal matrix rings from non-negative integer matrices. We also show that the principal factor matrix of a binary system of factors determine the structure of the system.

On the derived length of units in group algebra

Dishari Chaudhuri, Anupam Saikia (2017)

Czechoslovak Mathematical Journal

Let G be a finite group G , K a field of characteristic p 17 and let U be the group of units in K G . We show that if the derived length of U does not exceed 4 , then G must be abelian.

On the K -theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case

Patrick Polo (1995)

Annales de l'institut Fourier

Let G be a semisimple complex algebraic group and X its flag variety. Let 𝔤 = Lie ( G ) and let U be its enveloping algebra. Let 𝔥 be a Cartan subalgebra of 𝔤 . For μ 𝔥 * , let J μ be the corresponding minimal primitive ideal, let U μ = U / J μ , and let 𝒯 U μ : K 0 ( U m u ) be the Hattori-Stallings trace. Results of Hodges suggest to study this map as a step towards a classification, up to isomorphism or Morita equivalence, of the -algebras U μ . When μ is regular, Hodges has shown that K 0 ( U μ ) K 0 ( X ) . In this case K 0 ( U μ ) is generated by the classes corresponding to...

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