Geodesic
Convexity Conditions on f-Rings
Canadian journal of mathematics, Tome 38 (1986) no. 1, pp. 48-64

Voir la notice de l'article provenant de la source Cambridge University Press

Let n be a positive integer. An f-ring A is said to satisfy the left n th-convexity property if for any u, v ∊ A such that v ≧ 0 and 0 ≧ u ≧ vn , there exists a w ∊ A such that u = wv. The right n th-convexity property is defined similarly and an f-ring is said to satisfy the n th-convexity property if it satisfies both the left and the right n th-convexity property. In this paper, we study arbitrary f-rings which satisfy one of the convexity properties.Those f-rings which satisfy one or more of these properties have been studied by several authors. In [3, 1D], L. Gillman and M. Jerison note that any C(X) satisfies the n th-convexity property for all n ≧ 2, and in [3, 14.25], they give several properties that in C(X) are equivalent to the 1st-convexity property. M. Henriksen proves some results about the ideal theory of an f-ring satisfying the 2nd-convexity property in [5] and S. Steinberg studies left quotient rings of f-rings satisfying the left 1st-convexity property in [13]. 
Larson, Suzanne. Convexity Conditions on f-Rings. Canadian journal of mathematics, Tome 38 (1986) no. 1, pp. 48-64. doi: 10.4153/CJM-1986-003-6
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