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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.
Received: 02.01.1973
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
Linking options:
https://www.mathnet.ru/eng/sm3431https://doi.org/10.1070/SM1973v021n04ABEH002938 https://www.mathnet.ru/eng/sm/v134/i4/p550
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Abstract page: | 280 | Russian version PDF: | 119 | English version PDF: | 10 | References: | 48 |
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