martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. in this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

Martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. In this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

Models of intermittent behaviour are usually formulated using a set of multiplicative random weights on a Cayley tree. However, inter-mittency in particle multiproduction from QCD jets is related to fragmentation of an additive quantum number, e.g. energy-momentum. We exhibit the non-trivial stochastic mapping between these additive and multiplicative cascading processes.

there are several kinds of hyperrings, for example, krasnerhyperrings, multiplicative hyperring, general hyperrings and$h_v$-rings. in a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. in this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf keywords:} multiplic...

The Banach-Stone theorem states that any surjective, linear mapping T between spaces of continuous functions that satisfies ‖T (f)− T (g)‖ = ‖f − g‖, where ‖ · ‖ denotes the uniform norm, is a weighted composition operator. We study a multiplicative analogue, and demonstrate that a surjective mapping T , not necessarily linear, between algebras of continuous functions with ‖T (f)T (g)‖ = ‖fg‖ m...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

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Complex numerals (e.g., four hundred) have a multiplicative structure (four hundred = 4 x 100). This paper investigates whether children are sensitive to the meaning of the multiplicative structure. We designed a novel word learning paradigm and taught 4to 6-year-old children the meaning of a novel numeral phrase (e.g., ‘one gobi houses’ to mean a group of three houses). We then asked whether t...