Bg = Pg: a Success Story
نویسنده
چکیده
All semigroups and monoids except free monoids and free groups are assumed finite in this paper. A monoid M divides a monoid N if M is a quotient of a submonoid of N . The set of idempotents of a monoid M is denoted E(M). The word “variety” will be used for pseudo-variety — that is, a collection of finite monoids closed under division and finite direct product. A block group is a monoid such that every R-class (resp. L-class) contains at most one idempotent. Block groups form a variety of monoids, denoted BG, which is the topic of this paper. More precisely, we want to make some comments on the following cryptic line, which states that six apparently distinct varieties of monoids are in fact all equal:
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