Suppose F is any field and n is an integer with n ⩾ 4. Let K n ( F) be the set of all n × n alternate matrices over F, and let ( K n ( F), +, ·) be the non-associative ring formed by K n ( F) under the usual addition ‘+’ and the multiplication ‘·’ defined by X · Y = XYX for all X, Y ∈ K n ( F). A pair of n × n matrices ( A, B) is said to be rank-additive if rank( A + B) = rank A + rank B, and rank-subtractive if rank( A − B) = rank A − rank B. We say that an operator ϕ : K n ( F) → K n ( F) is additive if ϕ( X + Y) = ϕ( X) + ϕ( Y) for any X, Y ∈ K n ( F), a preserver of rank-additivity (respectively, rank-subtractivity) on K n ( F) if it preserves the set of all rank-additive (respectively, rank-subtractive) pairs, a preserver of rank on K n ( F) if rank ϕ( X) = rank X for every X ∈ K n ( F), and a ring endomorphism of ( K n ( F), +, ·) if it is additive and satisfies ϕ( X · Y) = ϕ( X) · ϕ( Y) for any X, Y ∈ K n ( F). We determine the general form of all additive preservers of rank (respectively, rank-additivity and rank-subtractivity) on K n ( F) and characterize all ring endomorphisms of ( K n ( F), +, ·).