OMOLOGII ȘI STRUCTURI ABSTRACTE

Abstract

Let R be a ring and G be an R-modul. Denote by S(X,G) the R-modul of all words with the
alphabet X and coeficients from G. System T = {En, hn: n N}it is called a sequence of oriented sets if: the
set E0 is non-empty and h0: E00 is a mapping; if n ≥ 1 and the set En is empty, then the set En+1 is empty
too; if n ≥ 1 and the set En is non-empty, then hn: EnS(En-1, G) is a mapping; if n ≥ 2, x En and hn(x) =
a1x1 +a2 x2 + ... +am xm, then the G-word hn-1(hn(x)) = a1hn1(x1) + a2hn-1(x2) + ... + am hn-1(xm) it is equivalent
with the word 0 from S(En2, G). We prepose a method of construction of homological groups and
cohomological groups applying the concept of the sequence of oriented sets.