Real algebra is a branch of algebra which studies formally real rings, i. e. commutative unital rings in which 1 is not a sum of squares. The most important invariant of a formally real ring A is its real spectrum Sper(A). The motivation for studying real algebra comes from semialgebraic geometry. Related areas of algebra are:
The main interest of the Slovenian real algebra group is noncommutative real algebra. An associative unital ring A is formally real if 1 is not a sum of permuted products of squares. Noncommutative formally real rings include:
