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.
@article{bwmeta1.element.bwnjournal-article-cmv79z2p241bwm,
author = {James Renshaw},
title = {On subrings of amalgamated free products of rings},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {241-248},
zbl = {0929.16022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv79z2p241bwm}
}
Renshaw, James. On subrings of amalgamated free products of rings. Colloquium Mathematicae, Tome 79 (1999) pp. 241-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv79z2p241bwm/
[000] [1] P. M. Cohn, On the free product of associative rings, Math. Z. 71 (1959), 380-398. | Zbl 0087.26303
[001] [2] J. M. Howie, Embedding theorems with amalgamation for semigroups, Proc. London Math. Soc. (3) 12 (1962), 511-534. | Zbl 0111.03702
[002] [3] J. M. Howie, Subsemigroups of amalgamated free products of semigroups, ibid. 13 (1963), 672-686. | Zbl 0124.01701
[003] [4] J. H. Renshaw, Extension and amalgamation in rings, Proc. Roy. Soc. Edinburgh Sect. A 102 (1986), 103-115. | Zbl 0589.16019
[004] [5] J. H. Renshaw, Extension and amalgamation in monoids and semigroups, Proc. London Math. Soc. (3) 52 (1986), 119-141. | Zbl 0546.20054
[005] [6] J. H. Renshaw, Perfect amalgamation bases, J. Algebra 141 (1991), 78-92. | Zbl 0735.20041
[006] [7] J. H. Renshaw, Subsemigroups of free products of semigroups, Proc. Edinburgh Math. Soc. (2) 34 (1991), 337-357. | Zbl 0752.20036
[007] [8] J. R. Rotman, An Introduction to Homological Algebra, Pure and Appl. Math. 85, Academic Press, New York, 1979. | Zbl 0441.18018