Power algebras over semifields and their applications (Q2717950)

Let \((F,+,\cdot)\) be a commutative semifield with absorbing zero \(0\). By a power algebra over \(F\) the author means the set \(F^A\) of all \(F\)-valued mappings on some non-empty set \(A\) together with pointwise operations. A lot of semirings appear in this way. Other interesting algebraic structures are obtained as power algebras if \(A\) itself is some algebra like a semigroup, a monoid, a group or a semiring, and additional operations on \(F^A\) are defined by the operations on \(A\). In his survey article the author presents several examples of this kind, together with many applications in different areas of pure and applied mathematics including linear algebra over semifields and idempotent analysis.