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Clash Royale CLAN TAG #URR8PPP up vote 4 down vote favorite Let L be modular lattice, M be lattice and $f:Lto M$ be a homomorphism. I want to show $f(L)$ is a modular lattice.. We already know that homomorphic image of lattice is lattice. So we only want to show that if $f(a)leq f(b)$ then $f(a) vee (f(x)wedge f(b))= (f(a)vee f(x))wedge f(b) $ for $a,b,x in L$ Since L is modular $aleq b$ implies $a vee(xwedge b)= (avee x)wedge b$ My problem is: I must begin with the assumption $f(a)leq f(b)$ then show $f(a) vee (f(x)wedge f(b))= (f(a)vee f(x))wedge f(b) $ for which I need to use $a vee(xwedge b)= (avee x)wedge b$ But $f(a)leq f(b)$ need not necessarily imply $aleq b$ since it is only homomorphism and not isomorphism. discrete-mathematics share | cite | improve this question asked 4 hours ago So Lo 591 1 8 add a comment  |  up vote 4 down vote favorite Let L be modular lattice, M be lattice and $...