let a be a unital r-algebra and m be a unital a-bimodule. it is shown that every jordan derivation of the trivial extension of a by m, under some conditions, is the sum of a derivation and an antiderivation.

Let A be a unital R-algebra and M be a unital A-bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation.

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 b...

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 b...

Recall that a ring $R\ $is said to be quasi regular if its total quotient $q(R)\ \textit{von Neumann regular}. It is well known and only it reduced satisfying the property: for each $a\in R,$ $ann_{R}(ann_{R}(a))=ann_{R}(b)$ some $b\in R$. Here, in this study, we extend notion of rings which satisfy aforementioned property modules. We give many characterizations properties these two classes Mor...

We consider a non-canonic field in the context of Starobinsky inflation. work Einstein-frame. In this frame, gravitational part action is equivalent to Hilbert–Einstein action, plus scalar called scalaron. investigate model with heavy scalaron trapped at effective potential minimum, where its fluctuations are negligible. To be more explicit, we Dirac–Born–Infeld (DBI) field, which usually consi...