Abstract
Let { R ~ } ~ A be a family of rings. Let us suppose that R~ ~ R~=B~ ~ B v ~ B andR is a subring of each ring of this family for arbitrary pairwise different ~, ~, w~ A . Then the set-theoretic union U~eAR~ of the rings R% is called their c~nalg~ (with the single amalgamated subring R). We will say that a variety of rings 8 has the property of embeddability of amalgams if each amalgam of rings from 8 can be embedded in a ring from ~. The problem of description of varieties of groups with similar property is given in [I] (Problem 6); it has been solved for the case of locally finite varieties by B. H. Neumann. M. V. Sapir has described locally finite varieties of semigroups 8, in which each amalgam (with the same amalgamated subsemigroup) can be embedded in a semigroup from 8. Let us also note the article [2] of T. E. Hall, devoted to the same problem for varieties of inverse semigroups.
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