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 Mat. Sb. (N.S.), 1973, Volume 92(134), Number 4(12), Pages 550–563 (Mi msb3431)

Boolean-valued algebras

V. N. Salii

Abstract: The paper contains the construction of a general theory of Boolean-valued algebras: There are introduced the notions of a homeomorphism, congruence, subalgebra and direct product. It is shown that these algebras possess properties that are totally analogous to the properties of two-valued algebras. To every Boolean-valued algebra $\mathfrak A$ there is related a certain universal algebra $\mathfrak{N(A)}$, called the normal extension of $\mathfrak A$, whose elements are all the partitions of unity of the given Boolean algebra, with naturally extended operations. The equational equivalence of an arbitrary Boolean-valued algebra and its normal extension is proved. It is shown that every homomorphism of a Boolean-valued algebra can be uniquely extended to a homomorphism of its normal extension.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 21:4, 544–557

Bibliographic databases:

UDC: 519.47
MSC: Primary 02J05, 02H10; Secondary 06A40, 08A05

Citation: V. N. Salii, “Boolean-valued algebras”, Mat. Sb. (N.S.), 92(134):4(12) (1973), 550–563; Math. USSR-Sb., 21:4 (1973), 544–557

Citation in format AMSBIB
\Bibitem{Sal73}
\by V.~N.~Salii
\paper Boolean-valued algebras
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 92(134)
\issue 4(12)
\pages 550--563
\mathnet{http://mi.mathnet.ru/msb3431}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=337576}
\zmath{https://zbmath.org/?q=an:0286.08006}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 21
\issue 4
\pages 544--557
\crossref{https://doi.org/10.1070/SM1973v021n04ABEH002938}