Contents
Research Article
On Numbers Generated by es(ex-1)
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- Published online by Cambridge University Press:
- 20 November 2018, pp. 751-754
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On the Distribution of Integer Solutions of f(x, y) = z2 for a Definite Binary Quadratic Form f
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- Published online by Cambridge University Press:
- 20 November 2018, pp. 755-756
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A Note on a Fully Ordered Ring
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- Published online by Cambridge University Press:
- 20 November 2018, pp. 757-758
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A ring R (associative ring) is said to be fully ordered provided that R is a linearly ordered set under a relation
such that for any a, b and c in R, 
implies that 
and if c ε 0 then 
and 
. We say a subset K of R is convex provided that if a, b ε K such that 
then the interval [a, b] is a subset of K. Obviously an additive subgroup K of R is convex if and only if b ε K and b > 0 implies [a, b] ⊆ K.
such that for any a, b and c in R, 
implies that 
and if c ε 0 then 
and 
. We say a subset K of R is convex provided that if a, b ε K such that 
then the interval [a, b] is a subset of K. Obviously an additive subgroup K of R is convex if and only if b ε K and b > 0 implies [a, b] ⊆ K.