Pseudo-Valuations on BE-Algebras
نویسنده
چکیده
Based on the Buşneag’s model ([2, 3, 4]), the notion of pseudovaluations (valuations) on a BE-algebra is introduced, and a pseudometric is induced by a pseudo-valuation on BE-algebras. Related properties are investigated, and conditions for a real-valued function on a BE-algebra to be a pseudo-valuation are discussed. Using the notion of (pseudo) valuation, we show that the binary operation in BE-algebras is uniformly continuous. Mathematics Subject Classification: 06F35, 03G25, 03C05
منابع مشابه
Quotient BCI-algebras induced by pseudo-valuations
In this paper, we study pseudo-valuations on a BCI-algebra and obtain some related results. The relation between pseudo-valuations and ideals is investigated. We use a pseudo-metric induced by a pseudovaluation to introduce a congruence relation on a BCI-algebra. We define the quotient algebra induced by this relation and prove that it is also a BCI-algebra and study its properties.
متن کاملBCC-algebras with pseudo-valuations
The notion of pseudo-valuations (valuations) on a BCC-algebra is introduced by using the Buşneag’s model ([1–3]), and a pseudo-metric is induced by a pseudo-valuation on BCC-algebras. Conditions for a real-valued function to be an BCK-pseudo-valuation are provided. The fact that the binary operation in BCC-algebras is uniformly continuous is provided based on the notion of (pseudo) valuation.
متن کاملFantastic Deductive Systems in Probability Theory on Generalizations of Fuzzy Structures
The aim of this paper is to introduce the notion of fantastic deductive systems on generalizations of fuzzy structures, and to emphasize their role in the probability theory on these algebras. We give a characterization of commutative pseudo-BE algebras and we generalize an axiom system consisting of four identities to the case of commutative pseudo-BE algebras. We define the fantastic deductiv...
متن کاملCommutative Pseudo valuations on BCK-Algebras
D. Buşneag 1 defined pseudo valuation on a Hilbert algebra and proved that every pseudo valuation induces a pseudometric on a Hilbert algebra. Also, D. Buşneag 2 provided several theorems on extensions of pseudo valuations. C. Buşneag 3 introduced the notions of pseudo valuations valuations on residuated lattices, and proved some theorems of extension for these using the model of Hilbert algebr...
متن کاملINITIAL RAMIFICATION INDEX OF NONINVARIANT VALUATIONS ON FINITE DIMENSIONAL DIVISION ALGEBRAS
Let D be a division ring with centre K and dim, D< ? a valuation on K and v a noninvariant extension of ? to D. We define the initial ramfication index of v over ?, ?(v/ ?) .Let A be a valuation ring of o with maximal ideal m, and v , v ,…, v noninvariant extensions of w to D with valuation rings A , A ,…, A . If B= A , it is shown that the following conditions are equivalent: (i) B i...
متن کامل