We show that any lexsegment ideal with linear resolution has linear quotients with respect to a suitable ordering of its minimal monomial generators. For completely lexsegment ideals with linear resolution we show that the decomposition function is regular. For arbitrary lexsegment ideals we compute the depth and the dimension. As application we characterize the Cohen--Macaulay lexsegment ideals.
"Properties of lexsegment ideals." Osaka J. Math. 47 (1) 67 - 87, March 2010.