On subrings of amalgamated free products of rings

• Autorzy: James Renshaw
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 79
• Numer: 2
• Strony: 241-248

Daty

wydano

1999

otrzymano

1998-03-30

poprawiono

1998-07-13

Twórcy

autor

James Renshaw

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

Bibliografia

• [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.