Enlargements, Semiabundancy and Unipotent Monoids1
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چکیده
The relation R̃ on a monoid S provides a natural generalisation of Green’s relation R. If every R̃-class of S contains an idempotent, S is left semiabundant; if R̃ is a left congruence then S satisfies (CL). Regular monoids, indeed left abundant monoids, are left semiabundant and satisfy (CL). However, the class of left semiabundant monoids is much larger, as we illustrate with a number of examples. This is the first of three related papers exploring the relationship between unipotent monoids and left semiabundancy. We consider the situations where the power enlargement or the Szendrei expansion of a monoid yields a left semiabundant monoid with (CL). Using the Szendrei expansion and the notion of the least unipotent monoid congruence σ on a 1991 Mathematics Subject Classification 20 M 10 This work was started as part of the JNICT contract PBIC/C/CEN/1021/92 and further supported by PRAXIS/2/2.1/MAT/73/94 and the British Council/JNICT protocol 1996/97. keywords: enlargement, expansion, semiabundant, unipotent 1
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تاریخ انتشار 2005