Let $k$ be a commutative ring and let $R$ be an associative (not necessarily commutative) $k$-algebra with unit. Also, let $M$ be an $R$-bimodule. It is well known that on $S:=R+M$ we can define an associative (unital) $k$-algebra structure, called the trivial extension of $R$ by $M$. The addition and multiplication by scalars are componentwise and the multiplication is $$(a,m)(b,n):=(ab, an+mb).$$ I would like to know if the projective (left, right, bi) modules over $S$ can be characterized in terms of the projective (left, right, bi) modules over $R$ and the properties of $M$.

Thank you.


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