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Special semigroups on the two-cell

1970
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Pacific Journal of Mathematics
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A commutative semigroup £ has property (α) if (1) S is topologically a two-cell, (2) S has no zero divisors, and (3) the boundary of S is the union of two unit intervals with the usual multiplication. A characterization of semigroups having property (a) will be given. Let (7, •) denote the closed unit interval with the usual multiplication. Let I be a closed ideal of (I, •) X (7, •) such that M contains (7 X {0}) u ({0} X 7), and M n (7 x {1}) = {(0,1)} or M n ({1} x 7) = {(1, 0)}. For each a,

doi:10.2140/pjm.1970.34.639
fatcat:j5xbvjijyzd6jia5bv534ablsi