Abstract
The purpose of this note is to generalize a theorem of Tamura’s [3] providing a self-contained and, we think, more elementary proof than Tamura’s in that it avoids using the theory of contents. Tamura’s result states that a semigroup S satisfies an identify xy=f(x,y) with f(x,y) a word of length greater than 2 which starts with y and ends in x if and only if S is an inflation of a semilattice of groups satisfying the same identity. We investigate semigroups as in Tamura’s Theorem, except that we permit f(x,y) to vary with x and y.
References
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Putcha, M.S. and J. Weissglass,A semilattice decomposition into semigroups having at most one idempotent, (to appear).
Tamura, T.,Semigroups satisfying identity xy=f(x,y), Pacific J. Math. 31 (1969), 513–521.
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Communicated by A.H. Clifford
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Putcha, M.S., Weissglass, J. Semigroups satisfying variable identities. Semigroup Forum 3, 64–67 (1971). https://doi.org/10.1007/BF02572943
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DOI: https://doi.org/10.1007/BF02572943