In this paper branching rules for the fundamental representations of the symplectic groups in positive characteristic are found. The submodule structure of the restrictions of the fundamental modules for the group Sp2n(K) to the naturally embedded subgroup Sp2n−2(K) is determined. As a corollary, inductive systems of fundamental representations for Sp∞(K) are classified. The submodule structure...

In previous research we extended the submodule construction techniques to cover a more expressive and compact behavioral model that handles data through parameterized interactions, state variables, and simple transition guards. The model was based on extended Input/Output Automata, and the algorithm on the Chaos concept. In this paper we generalize these extensions and improve the submodule con...

We introduce an extension of the derivatives of rational expressions to expressions denoting formal power series over partially commuting variables. The expressions are purely noncommutative, however they denote partially commuting power series. The derivations (which are so-called φ-derivations) are shown to satisfy the commutation relations. Our main result states that for every so-called rig...

The submodule construction problem (SCP) as stated and formulated by Merlin and Bochmann [P. Merlin, G.V. Bochmann, On the construction of submodule specification and communication protocols, ACM Trans. Prog. Lang. Sys., 5(1) (1983) 1–25] is considered: given the specification of a system (module) and that of its n 2 1 submodules, determine the specification of the nth submodule that together w...

Let be a module over commutative ring with identity. Before studying the concept of Strongly Pseudo Nearly Semi-2-Absorbing submodule, we need to mention ideal and basics that you study submodule. Also, introduce several characteristics submodule in classes multiplication modules other types modules. We also had no luck because is not ideal. it noted under conditions, which this faithful module...

In this paper we study certain families of right ideals in noncommutative rings, called right Oka families, generalizing previous work on commutative rings by T.Y. Lam and the author. As in the commutative case, we prove that the right Oka families in a ring R correspond bijectively to the classes of cyclic right R-modules that are closed under extensions. We define completely prime right ideal...

Let Λ be a commutative local uniserial ring of length n, p a generator of the maximal ideal, and k the radical factor field. The pairs (B, A) where B is a finitely generated Λ-module and A ⊆ B a submodule of B such that pmA = 0 form the objects in the category Sm(Λ). We show that in case m = 2 the categories Sm(Λ) are in fact quite similar to each other: If also ∆ is a commutative local uniseri...