Semigroups with Quasi-Zeroes
1980 ◽
Vol 32
(3)
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pp. 511-530
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Let S be a semigroup. An element a ∈ S is said to be a left quasi-zero if <a>x ⋂ <a> ≠ ∅ for all x ∈ S, where <a> denotes the cyclic sub-semigroup of S generated by a. In a recent study [6] of semigroups with a maximum right congruence, such elements proved to be useful in providing characterizations of these semigroups. Left quasizeroes have appeared in the literature under different names in a variety of situations. In the context of semigroup radicals, left quasi-zeroes are called right quasi-regular elements, where an element is defined to be right quasi-regular if it is not a left identity for any right congruence other than the universal congruence (see [4], [5], [2], [7], and [8]).
1996 ◽
Vol 11
(18)
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pp. 3257-3295
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1979 ◽
Vol 20
(2)
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pp. 125-128
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2001 ◽
Vol 27
(6)
◽
pp. 387-389
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1978 ◽
Vol 25
(1)
◽
pp. 45-65
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2017 ◽
Vol 23
(3)
◽
pp. 311-320
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Keyword(s):