University of Guilan Journal of Algebra and Related Topics 2345-3931 1 1 2013 11 01 On continuous cohomology of locally compact Abelian groups and bilinear maps 67 77 46 EN H. Sahleh University of Guilan Journal Article 2013 08 24 Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can be embedded in the second bilinear cohomology. https://jart.guilan.ac.ir/article_46_2de2cc9120ea26c74a54f5b4acc2febf.pdf