Generalized semigroups of quotients
Author:
C. V. Hinkle
Journal:
Trans. Amer. Math. Soc. 183 (1973), 87117
MSC:
Primary 20M10
MathSciNet review:
0335666
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Abstract: For S a semigroup with 0 and a right Sset, certain classes of sub Ssets called right quotient filters are defined. A study of these right quotient filters is made and examples are given including the classes of intersection large and dense sub Ssets respectively. The general semigroup of right quotients Q corresponding to a right quotient filter on a semigroup S is developed and basic properties of this semigroup are noted. A nonzero regular semigroup S is called primitive dependent if each nonzero right ideal of S contains a 0minimal right ideal of S. The theory developed in the paper enables us to characterize all primitive dependent semigroups having singular congruence the identity in terms of subdirect products of column monomial matrix semigroups over groups.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197303356666
PII:
S 00029947(1973)03356666
Keywords:
Semigroups of quotients,
singular congruences,
Rees matrix semigroups,
primitive dependent semigroups
Article copyright:
© Copyright 1973
American Mathematical Society
