In this paper, we introduce the notionofWajsberg implicative ideal(WI-ideal)of lattice Wajsberg algebra.Further, we definelattice H-Wajsberg algebra, implication homomorphismand lattice implication homomorphism oflattice Wajsberg algebra. Finally, we give kernel of implication homomorphism and obtain some oftheir properties.

In this paper we introduced homomorphism, strong homomorphism in bipolar fuzzy finite state machines and discuss their properties using bipolar-valued fuzzy set. Mathematics Subject Classification: 18B20, 68Q45, 68Q70, 03E72

Let $A$ and $B$ be two unital $C^{*}$-algebras and $varphi:A rightarrow B$ be a linear map. In this paper, we investigate the structure of linear maps between two $C^{*}$-algebras that preserve a certain property or relation. In particular, we show that if $varphi$ is unital, $B$ is commutative and $V(varphi(a)^{*}varphi(b))subseteq V(a^{*}b)$ for all $a,bin A$, then $varphi$ is a $*$-homomorph...

It is not difficult to see that every group homomorphism from Z to R extends to a homomorphism from R to R. We discuss other examples of discrete subgroups Γ of connected Lie groups G, such that the homomorphisms defined on Γ can (“virtually”) be extended to homomorphisms defined on all of G. For the case where G is solvable, we give a simple proof that Γ has this property if it is Zariski dens...

In this paper we construct new obstructions for the surjectivity of the Johnson homomorphism of the automorphism group of a free group. We also determine the structure of the cokernel of the Johnson homomorphism for degree 2 or 3.