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Idempotent-separating extensions of regular semigroups with Abelian kernel

  • M. Loganathan (a1)

Abstract

Let S be a regular semigroup and D(S) its associated category as defined in Loganathan (1981). We introduce in this paper the notion of an extension of a D(S)-module A by S and show that the set Ext(S, A) of equivalence classes of extensions of A by S forms an abelian group under a Baer sum. We also study the functorial properties of Ext(S, A).

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References

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Lallement, G. (1967), ‘Demi-groupes réguliers’, Ann. Mat. Pura Appl. 87, 47130.
Lausch, H. (1975), ‘Cohomology of inverse semigroups’, J. Algebra 35, 273303.
Leech, J. (1975), ‘H-coextensions of monoids’, Mem. Amer. Math. Soc. 1, no. 157 (Amer. Math. Soc., Providence, R.I..).
Loganathan, M. (1981), ‘Cohomology of inverse semigroups’, to appear.
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Nambooripad, K. S. S. (1979), ‘Structure of regular semigroups I’, Mem. Amer. Math. Soc. 22, no. 224 (Amer. Math. Soc., Providence, R.I.).
Sribala, S. (1977), ‘Cohomology and extension of inverse semigroup’, J. Algebra 47, 117.
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