%0 Journal Article %T HOOPS WITH QUASI-VALUATION MAPS %J Journal of Algebraic Systems %I Shahrood University of Technology %Z 2345-5128 %A Aaly Kologani, M. %A Rezaei, G. R. %A Borzooei, R. A. %A Jun, Y. B. %D 2021 %\ 01/01/2021 %V 8 %N 2 %P 251-268 %! HOOPS WITH QUASI-VALUATION MAPS %K Hoop %K quasi-valuation map %K SāŠ™(Sā†’ %K F)-quasi-valuation map %K (pseudo) metric space %R 10.22044/jas.2020.8499.1413 %X Based on subalgebras and filters in hoops, the notions of S-quasi-valuation maps and F-quasi-valuation maps are introduced, and related properties are investigated. Relations between S-quasi-valuation maps and F-quasi-valuation maps are introduced. Using F-quasi-valuation map, a (pseudo) metric space is indued, and we show that the operations “āŠ™”, “→” and “∧” in a hoop are uniformly continuous. %U https://jas.shahroodut.ac.ir/article_1955_ce7dc383760b98c224e268740b53e849.pdf