论文信息 - Biordered Sets Come from Semigroups

Biordered Sets Come from Semigroups

Information about a semigroup can often be gleaned from its partial algebra of idempotents. For example, the idempotents of an inverse semigroup form a semilattice. All isomorphisms between principal ideals of a semilattice E form the Munn inverse semigroup T,, which contains the fundamental image of every inverse semigroup whose idempotents form the semilattice E [ll, 123. Thus semilattices give rise to all fundamental inverse semigroups. Successful efforts have been made to generalize the Munn construction to the wider class of regular semigroups [ 1,6-9, 13, 141. Nambooripad achieved this using the concept of a regular biordered set. The biordered set of a semigroup S means simply the partial algebra consisting of the set E = E(S) of idempotents of S with multiplication restricted to

David Easdown | D. Easdown

[1] K. Nambooripad. Structure of regular semigroups , 1979 .

[2] UNIFORM SEMILATTICES AND BISIMPLE INVERSE SEMIGROUPS , 1966 .

[3] The fundamental representation of a regular semigroup , 1975 .

[4] M. Petrich. Structure of regular semigroups , 1971 .

[5] A. Clifford,et al. The algebraic theory of semigroups , 1964 .

[6] David Easdown. BIORDERED SETS ARE BIORDERED SUBSETS OF IDEMPOTENTS OF SEMIGROUPS , 1984 .

[7] T. Hall. On regular semigroups , 1973 .

[8] A new proof that regular biordered sets come from regular semigroups , 1984 .

[9] K. Nambooripad. Structure of regular semigroups, I fundamental regular semigroups , 1974 .

[10] The structure of regular semigroups, II: Cross-connections , 1974 .

[11] P. A. Grillet. The structure of regular semigroups, I: A representation , 1974 .

[12] W. Munn. FUNDAMENTAL INVERSE SEMIGROUPS , 1970 .

[13] J. Howie. An introduction to semigroup theory , 1976 .

[14] F. Pastijn,et al. The biorder on the partial groupoid of idempotents of a semigroup , 1980 .