Matrices of bisimple regular semigroups |
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Authors: | Janet E Mills |
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Institution: | (1) Department of Mathematics and Computer Science, James Madison University, 22807 Harrisonburg, Virginia |
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Abstract: | A semigroup S is a matrix of subsemigroups Siμ, i ε I, μ ε M if the Siμ form a partition of S and SiμSjν≤Siν for all i, j in I, μ, ν in M. If all the Siμ are bisimple regular semigroups, then S is a bisimple regular semigroup. Properties of S are considered when the Siμ are bisimple and regular; for example, if S is orthodox then each element of S has an inverse in every component Siμ. |
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