Inverse semigroups generated by nilpotent transformations
1984 ◽
Vol 99
(1-2)
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pp. 153-162
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Keyword(s):
Index 2
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SynopsisLet X be a set with infinite cardinality m and let B be the Baer-Levi semigroup, consisting of all one-one mappings a:X→X for which ∣X/Xα∣ = m. Let Km=<B 1B>, the inverse subsemigroup of the symmetric inverse semigroup ℐ(X) generated by all products β−γ, with β,γ∈B. Then Km = <N2>, where N2 is the subset of ℐ(X) consisting of all nilpotent elements of index 2. Moreover, Km has 2-nilpotent-depth 3, in the sense that Let Pm be the ideal {α∈Km: ∣dom α∣<m} in Km and let Lm be the Rees quotient Km/Pm. Then Lm is a 0-bisimple, 2-nilpotent-generated inverse semigroup with 2-nilpotent-depth 3. The minimum non-trivial homomorphic image of Lm also has these properties and is congruence-free.
1981 ◽
Vol 31
(4)
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pp. 415-420
Keyword(s):
2011 ◽
Vol 21
(01n02)
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pp. 315-328
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1978 ◽
Vol 19
(1)
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pp. 59-65
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Keyword(s):
1987 ◽
Vol 29
(1)
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pp. 21-40
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2008 ◽
Vol 85
(1)
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pp. 75-80
1983 ◽
Vol 93
(3-4)
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pp. 245-257
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Keyword(s):
2008 ◽
Vol 51
(2)
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pp. 387-406
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Keyword(s):
1987 ◽
Vol 43
(1)
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pp. 81-90
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2008 ◽
Vol 45
(3)
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pp. 395-409
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