On the monoid of cofinite partial isometries of $\qq{N}^n$ with the usual metric
2019 ◽
Vol 12
(3)
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pp. 51-68
Keyword(s):
In this paper we study the structure of the monoid Iℕn ∞ of cofinite partial isometries of the n-th power of the set of positive integers ℕ with the usual metric for a positive integer n > 2. We describe the group of units and the subset of idempotents of the semigroup Iℕn ∞, the natural partial order and Green's relations on Iℕn ∞. In particular we show that the quotient semigroup Iℕn ∞/Cmg, where Cmg is the minimum group congruence on Iℕn ∞, is isomorphic to the symmetric group Sn and D = J in Iℕn ∞. Also, we prove that for any integer n ≥2 the semigroup Iℕn ∞ is isomorphic to the semidirect product Sn ×h(P∞(Nn); U) of the free semilattice with the unit (P∞(Nn); U) by the symmetric group Sn.
1991 ◽
Vol 14
(3)
◽
pp. 457-462
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Keyword(s):
1961 ◽
Vol 5
(1)
◽
pp. 35-40
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2018 ◽
Vol 11
(04)
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pp. 1850056
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Keyword(s):
2021 ◽
Vol 14
(2)
◽
pp. 380-395
2009 ◽
Vol DMTCS Proceedings vol. AK,...
(Proceedings)
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