论文信息 - Generators and factorisations of transformation semigroups

Generators and factorisations of transformation semigroups

If E is the set of idempotents and G the group of units within a full transformation semigroup ℐ x , then EG = GE = ℐ x if X is finite. The question of identifying the subsemigroup EG = GE = 〈G∪E〉 in the case where X is infinite leads to an investigation of interrelations among various naturally occurring subsemigroups of ℐ X . In the final section it is shown that precisely two additional elements µ, v are needed in order that G∪E∪{µ, v} should generate ℐ x .

[1] Rob Carscadden. The Orbit Structure of Finite Monoids , 1993, Int. J. Algebra Comput..

[2] A semigroup approach to linear algebraic groups , 1983 .

[3] Peter M. Higgins,et al. Techniques of semigroup theory , 1991 .

[4] H. Mitsch,et al. A natural partial order for semigroups , 1986 .

[5] John Fountain,et al. Products of idempotent endomorphisms of an independence algebra of infinite rank , 1993 .

[6] Some subsemigroups of infinite full transformation semigroups , 1981 .

[7] J. Howie. Fundamentals of semigroup theory , 1995 .

[8] Normal semigroups of one-to-one transformations , 1991 .

[9] Richard M. Wilson,et al. A course in combinatorics , 1992 .

[10] K. Nambooripad,et al. The natural partial order on a regular semigroup , 1980, Proceedings of the Edinburgh Mathematical Society.

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

[12] J. Howie,et al. The Subsemigroup Generated By the Idempotents of a Full Transformation Semigroup , 1966 .