ArticleOriginal scientific text

Title

On subrings of amalgamated free products of rings

Authors 1

Affiliations

  1. Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, England

Abstract

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.

Bibliography

  1. P. M. Cohn, On the free product of associative rings, Math. Z. 71 (1959), 380-398.
  2. J. M. Howie, Embedding theorems with amalgamation for semigroups, Proc. London Math. Soc. (3) 12 (1962), 511-534.
  3. J. M. Howie, Subsemigroups of amalgamated free products of semigroups, ibid. 13 (1963), 672-686.
  4. J. H. Renshaw, Extension and amalgamation in rings, Proc. Roy. Soc. Edinburgh Sect. A 102 (1986), 103-115.
  5. J. H. Renshaw, Extension and amalgamation in monoids and semigroups, Proc. London Math. Soc. (3) 52 (1986), 119-141.
  6. J. H. Renshaw, Perfect amalgamation bases, J. Algebra 141 (1991), 78-92.
  7. J. H. Renshaw, Subsemigroups of free products of semigroups, Proc. Edinburgh Math. Soc. (2) 34 (1991), 337-357.
  8. J. R. Rotman, An Introduction to Homological Algebra, Pure and Appl. Math. 85, Academic Press, New York, 1979.
Pages:
241-248
Main language of publication
English
Received
1998-03-30
Accepted
1998-07-13
Published
1999
Exact and natural sciences