We present an example of a zero-dimensional F-space that is not strongly zero-dimensional.

Let k be a perfect field of characteristic p > 0. Using Dieudonné modules, we describe the exact conditions under which a Witt subgroup, i.e., a finite subgroup scheme of Wn, lifts to the ring of Witt Vectors W (k).

dis4, M. S. Robinson1, B. W. Denevi1, T. A. Giguere5, B. L. Jolliff6, S. E. Braden1, and the LROC Science Team. 1School of Earth and Space Exploration, Arizona State University, Tempe, AZ [email protected] 3Hawaii Institute of Geophysics and Planetology, University of Hawaii at Manoa, Honolulu, HI 4United States Geological Survey, As­ trogeology Program, Flagstaff, AZ 5Intergraph Corporation, H...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

Let R be a commutative ring with non-zero identity. The annihilator-inclusion ideal graph of R , denoted by ξR, is a graph whose vertex set is the of allnon-zero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacentif and only if either Ann(I) ⊆ J or Ann(J) ⊆ I. In this paper, we investigate the basicproperties of the graph ξR. In particular, we showthat ξR is a connected grap...

jahanshahloo has suggested a method for the solving linear programming problems with zero-one variables‎. ‎in this paper we formulate fully fuzzy linear programming problems with zero-one variables and a method for solving these problems is presented using the ranking function and also the branch and bound method along with an example is presented.

In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...