A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semi...A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semigroup is obtained. Munn(1966) gave a fundamental inverse semigroup. Following Munn's idea, we give a fundamental normal orthodox semigroup with an inverse transversal.展开更多
Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-...Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-related if Ker pO = Ker θ°, where p°= p｜s°. Expressions for the least and the greatest congruences in the same K°-class as p are provided. A number of equivalent conditions for K° being a congruence are given.展开更多
文摘A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semigroup is obtained. Munn(1966) gave a fundamental inverse semigroup. Following Munn's idea, we give a fundamental normal orthodox semigroup with an inverse transversal.
文摘Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-related if Ker pO = Ker θ°, where p°= p｜s°. Expressions for the least and the greatest congruences in the same K°-class as p are provided. A number of equivalent conditions for K° being a congruence are given.
基金Research is supported by National Science Foundation (19970128) of ChinaNatural Science Foundations[(011438)(021073),(Z02017)]Guangdong Province,China.The author would like to express his appreciation to Professor Y.Q.Guo for his help
基金Research is supported by National Natural Science Foundation (No.19970128) of ChinaNatural Science Foundations of Guangdong Province China(No.011438,021073,Z02017).
