abstract. let $l$ be a lattice with the least element $0$. an element $xin l$ is a zero divisor if $xwedge y=0$ for some $yin l^*=lsetminus left{0right}$. the set of all zero divisors is denoted by $z(l)$. we associate a simple graph $gamma(l)$ to $l$ with vertex set $z(l)^*=z(l)setminus left{0right}$, the set of non-zero zero divisors of $l$ and distinct $x,yin z(l)^*$ are adjacent if and only...

in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. in particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. then we study fuzzy...

x-ray diffraction peak profile analysis was used to identify changes in the lattice distortions during isothermal aging of fe-10ni-7mn (wt. %) maraging steel. integral peak breadths were analyzed using classical williamson-hall equation taking the elastic anisotropy into account. it was found that substantial lattice distortions rise during precipitation hardening which depend strongly on the s...

in this paper we give an elementary argument about the atoms and coatoms of the latticeof all subgroups of a group. it is proved that an abelian group of finite exponent is strongly coatomic.

the aim of this paper is to extend results established by h. onoand t. kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. the main theorem states that a residuatedlattice a is directly indecomposable if and only if its boolean center b(a)is {0, 1}. we also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...