No abstract

Em Ua and Da semigroups are defined by extrapolating the definitions of their group counterparts; and a class n semigroup is defined to be a subsemigroup of a class « group. The purpose of this paper is to show that a class n Ea semigroup generates an Ea group and that a class n semigroup is Ua if and only if it generates a Ua group.

“Sneaky Squares” are versions of a type of magic square introduced in an article by Martin Gardner many years ago (Scientific American, January 1957, pp. 138–42). His main example was that of a square using whole numbers under addition. As Gardner indicated, it is possible to construct such squares using addition or multiplication and to involve whole numbers, integers, rational numbers, or decimals. With a little variation, subtraction and division can also be involved. Thus Sneaky Squares can be conveniently used for a variety of basic drill work at all grade levels.

Abstract.Em Ua and Da semigroups are defined by extrapolating the definitions of their group counterparts; and a class n semigroup is defined to be a subsemigroup of a class « group. The purpose of this paper is to show that a class n Ea semigroup generates an Ea group and that a class n semigroup is Ua if and only if it generates a Ua group.