Some Semigroups on the Two-Cell

Lester, Anne E.

doi:10.2307/2033669

Cited by 5 publications

(3 citation statements)

References 1 publication

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“…The first three conclusions follow from [4, Theorem 3.1] and Theorem 2.1, where \p = wa. They can also be established by using the results and methods in [8] or [6]. The last result is a consequence of [4, Theorem 3.4], Theorem 2.1, and the fact that the only subunithetic semigroups on [0, 1 ] are the {/-semigroup and C-semigroup (see [2]).…”

Section: Proofmentioning

confidence: 94%

On compact divisible abelian semigroups

Hildebrant¹

1968

Proc. Amer. Math. Soc.

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The algebraic structure of divisible abelian semigroups has been studied in [9] and [l]. Some results on the topological and algebraic structure of compact uniquely divisible abelian semigroups have been obtained in [4] and [5]. A statement of equivalent conditions for a compact abelian semigroup to be divisible is presented in the present paper. Some of the results in [4] are extended to subunithetic semigroups, which are the fundamental building blocks of a divisible abelian semigroup.

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Section: Proofmentioning

confidence: 94%

On compact divisible abelian semigroups

Hildebrant¹

1968

Proc. Amer. Math. Soc.

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“…Such a sequence exists by Lemma 1. Let Z({pn}) be defined as in [5] and let e be the idempotent in Z({pn}). The author proves in [5] that e acts as a two-sided identity for all of {pn} and, in particular ep = p = pe which is as required by the lemma.…”

mentioning

confidence: 99%

“…In this example, for a£5\P, the representation of a = 6/ for 6£P and tET is unique. In [5], the author gives an example of such a semigroup described above but in it there exists an element in S\K for which this representation is not unique.…”

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confidence: 99%

Some semigroups on an 𝑛-cell

Hudson¹

1961

Trans. Amer. Math. Soc.

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The purpose of this paper is to prove a theorem which is a generalization of a theorem proved by the author in [5]. The latter theorem is a special case of the one presented here. The theorem to be proved is: Theorem. Let S be a semigroup which is topologically a closed n-cell, m ^2. Suppose for x and y in B, the bounding in-\)-sphere of S, xy = x. Then: (1) If S = K, the minimal ideal of S, then S consists entirely of left zeros, that is, xS = x for each x in S. (2) If S^K, then K is a deformation retract of S and K consists entirely of left zeros for S. Also there exists in S an I-semigroup T with the following properties : (i) S\K" = BT, where K° denotes the interior of K.

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The universal compact subunithetic semigroup

Hildebrant¹

1969

Proc. Amer. Math. Soc.

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Some Semigroups on the Two-Cell

Cited by 5 publications

References 1 publication

On compact divisible abelian semigroups

On compact divisible abelian semigroups

Some semigroups on an 𝑛-cell

The universal compact subunithetic semigroup

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