Normality in real AW*-algebras

S. A. Chepukhalin^ab, A. A. Rakhimov<sup>c

a</sup> Tashkent University of Information Technology
^b Plekhanov Russian State University of Economics, Moscow
^c National University of Uzbekistan named after Mirzo Ulugbek, Tashkent

Abstract: This paper is devoted to the study of the concept of normality in real AW*-algebras. The authors examine whether normality is preserved when passing from a complex AW*-algebra to its real part and prove that all real AW*-factors are normal. Conditions are established under which a real AW*-algebra is normal, in particular, when its center is locally $\sigma$-finite. The obtained results serve as real analogs of known theorems on normality in AW*-algebras and contribute to the development of operator algebra theory in the real setting.

Keywords: real AW*-algebra, normality, factor, monotone completeness, $\sigma$-finiteness, annihilator, projection

UDC: 517.98

MSC: 46L10, 46K10, 46L05

DOI: 10.36535/2782-4438-2025-243-78-80