Posets and differential graded algebras

If P is a partially ordered set and R is a commutative ring, then a certain differential graded /f-algebra A,(P) is defined from the order relation on P. The algebra A.(Vi) corresponding to the empty poset is always contained in A.(P) so that A,(P) can be regarded as an /4.(0)-algebra. The main result of this paper shows that if R is an integral domain and P and P' are finite posets such that A.(P) = A.(P') as differential graded /4,(0)-algebras, then P and P' are isomorphic. 1991 Mathematics subject classification (Amer. Math. Soc): primary 06A06.