Greens relations on the partition monoid and several related monoids
نویسندگان
چکیده
We describe Greens relations on the partition monoid, two of its submonoids, and the related Jones and Brauer monoids. Key Words: partition monoid, Jones monoid, ideal structure 2000 Mathematics Subject Classi cation: 20M20 1 The partition monoid and some submonoids The elements of the partition monoid Pn [5, 8, 9] are equivalence classes of graphs on a vertex set n [ n0 = f1; 2; :::ng [ f10; 20; :::n0g (consisting of two copies of n). Two such graphs are regarded as equivalent if they have the same connected components. We will thus select as a standard representative of each equivalence class a graph whose every component is a complete graph. However it facilitates visualisation to draw the graphs with a minimal number of edges, and we follow this convention in the diagrams below; however we should remember that each component is really a complete graph. Fig. 1 Multiplication in P6
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