of generators T (s) ij with s = 1, 2 , . . . and i , j = 1 , . . . , N is given by (1.1), (1.2). Comultiplication ∆ : Y(glN ) → Y(glN )⊗Y(glN ) is defined by (1.1), (1.16). The algebra Y(glN ) admits an alternative definition in terms of the ascending chain U(gl1) ⊂ U(gl2) ⊂ . . . of classical universal enveloping algebras [O]. For any non-negative integer M consider the commutant in U(glM+N ) ...

This equation was introduced in [Agu00, Agu01] and independently in [Pol00]. The algebraic meaning of this equation, explained in [Agu00, Agu01], is as follows. An associative algebra A is called an infinitesimal bialgebra if it is equipped with a coassociative coproduct which is a derivation, i.e. ∆(ab) = (a⊗ 1)∆(b)+∆(a)(1⊗b). This notion was introduced by Joni and Rota [RJ79] and is useful in...

The double Schur functions form a distinguished basis of the ring Λ(x ||a) which is a multiparameter generalization of the ring of symmetric functions Λ(x). The canonical comultiplication on Λ(x) is extended to Λ(x ||a) in a natural way so that the double power sums symmetric functions are primitive elements. We calculate the dual Littlewood–Richardson coefficients in two different ways thus pr...

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)ysubseteq P$ for $x, yin M$, implies that $xin P$ or $yin P$. In this paper, we study more properties of strongly prime submodules. It is shown that a finitely generated $R$-module $M$ is Artinian if and only if $M$ is Noetherian and every st...