Some semigroups on the two-cell

Lester, Anne E.

doi:10.1090/s0002-9939-1959-0106968-1

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Preliminary Results1

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1968

1988

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Cited by 20 publications

(3 citation statements)

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“…Inductively, xll2"y = 0. Since the cluster points of the sequence {x1'2"} are known to form a subgroup of 77 (1), [14], it follows that y=0, which completes the proof. Theorem 3.2.…”

mentioning

confidence: 64%

Linear Representations of Certain Compact Semigroups

Brown¹,

Friedberg²

1971

Transactions of the American Mathematical Society

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“…Inductively, xll2"y = 0. Since the cluster points of the sequence {x1'2"} are known to form a subgroup of 77 (1), [14], it follows that y=0, which completes the proof. Theorem 3.2.…”

mentioning

confidence: 64%

Linear Representations of Certain Compact Semigroups

Brown¹,

Friedberg²

1971

Transactions of the American Mathematical Society

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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: Preliminary Resultsmentioning

confidence: 94%

On Compact Divisible Abelian Semigroups

Hildebrant¹

1968

Proceedings of the American Mathematical Society

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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. Preliminary results.Notation. Throughout this paper N denotes the set of all positive integers, R denotes the set of all positive rational numbers, and R~d enotes the additive semigroup of all nonnegative real numbers.Definition.An element x in a semigroup S is said to be Proof. Since 5 is divisible and abelian, each bonding map T^ is an onto homomorphism.It follows that S* is a compact abelian semigroup.

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“…For example semigroups on the unit interval with identities are completely classified in [3], [4], and [7]. Some special cases on the two-cell have also been investigated [1], [2], [5], [6] and [7].…”

mentioning

confidence: 99%

Special semigroups on the two-cell

DeVun¹

1970

Pacific J. Math.

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Some semigroups on the two-cell

Cited by 20 publications

References 5 publications

Linear Representations of Certain Compact Semigroups

Linear Representations of Certain Compact Semigroups

On Compact Divisible Abelian Semigroups

Special semigroups on the two-cell

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