Semi-ideal Convex Effect Algebras

In this paper, we first construct a convex structure by ideals of effect algebras. Then we discuss convex properties of morphisms and monomorphisms between effect algebras. Further, we prove that partial binary operations \(\oplus\) $\oplus$ and \(\ominus\) $\ominus$ are separately convexity-preserving for the first position with respect to ideal convex structures when the effect algebra is a lattice effect algebra. A lattice effect algebra equipped with an ideal convex structure is called a semi-ideal convex effect algebra. Finally, we obtain that finite product and quotient of semi-ideal convex effect algebras are also semi-ideal convex effect algebras.