a. khalaf

The structure of an α(β,β) -topological ring is richer in comparison with the structure of an α(β,β) -topological group. The theory of α(β,β) -topological rings has many common features with the theory of α(β,β) -topological groups. Formally, the theory of α(β,β) -topological abelian groups is included in the theory of α(β,β) -topological rings. The purpose of this paper is to introduce and study the concepts of α(β,β) -topological rings and α(β,γ) -topological R-modules. we show how they may be introduced by specifying the neighborhoods of zero, and present some basic constructions. We provide fundamental concepts and basic results on α(β,β) -topological rings and α(β,γ) -topological Rmodules.

Milk samples in an aseptic manner at the beginning of dry period and three days after parturition from 124 mammary quarters (37 cows) were collected to determine somatic cell count (SCC). All quarters were scored (1 to 5)on the basis of teat–end hyperkeratosis to establish a correlation between the score and new infection rate andSCCs. After the last milking, a commercial intramammary antibiotic was used for all quarters. In this study criticalvalue of 250000 cell/ml was set for SCCs. Samples with somatic cell count lower and greater than this critical valuewere considered healthy and infected respectively. The statistical analysis showed 26.5 % new infection rate and5% cure rate at 3 days after parturition. The score were 1, 2, 3 and greater than 3 for 40%, 36%, 21% and 3% ofevaluated teats respectively. There was signifcant difference between milk SCC at the beginning of the dry periodand SCC of three days after parturition (p=0.0005, r = 0.8) Statistical analysis also showed signifcant differencesbetween teat-end hyperkeratosis and SCC at the same periods (p=0.0005, r = 0.66).There was no signifcant differences between teat score and new infection rate (P>0.05).