in this paper, we give a characterization of strongly jordan zero-product preserving maps on normed algebras as a generalization of  jordan zero-product preserving maps. in this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly jordan zero-product preserving maps are completely different. also, we prove that the direct p...

The purpose of this note is to describe when a general complex algebraic $^*$-algebra pre-$C^*$-normed, and investigate their structure the $^*$-algebras are Baer $^*$-rings in addition algebraicity. As main result we prove following theorem for $^*$-algebras: every kind can be decomposed as direct sum $M\oplus B$, where $M$ finite dimensional $B$ commutative $^*$-algebra. summand $^*$-isomorph...