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 O∗ be the C-algebra defined as the direct sum of all Cuntz algebras. Then O∗ has a non-cocommutative comultiplication ∆φ and a counit ε. Let BI(O∗) denote the set of all closed biideals of the C-bialgebra (O∗,∆φ, ε) and let P(P) denote the power set of the set of all prime numbers. We show a one-to-one correspondence between BI(O∗) and P(P). Furthermore, we show that for any I in BI(O∗), th...

We give a new realization of Y (sl3) via Cartan–Weyl elements. An algebraic description of Yangian Double DY (sl3), explicit comultiplication formulas and universal R-matrix are obtained in these terms.

abstract. let (r,p) be a noetherian unique factorization do-main (ufd) and m be a finitely generated r-module. let i(m)be the first nonzero fitting ideal of m and the order of m, denotedord_r(m), be the largest integer n such that i(m) ⊆ p^n. in thispaper, we show that if m is a module of order one, then either mis isomorphic with direct sum of a free module and a cyclic moduleor m is isomorphi...

The purpose of this paper is to give definitions of some new Hopf algebras analogous to the mod-p Steenrod algebras. For example, we produce a Hopf algebra over the integers whose reduction mod-p is the mod-p Steenrod algebra. Just for fun, we “quantize” these algebras too! Further study of the examples of this paper will be done in part II. 1 Deformations of Hopf Algebras Suppose that k is a c...

Complex diseases are presumed to be the results of the interaction of several genes and environmental factors, with each gene only having a small effect on the disease. Mapping complex disease genes therefore becomes one of the greatest challenges facing geneticists. Most current approaches of association studies essentially evaluate one marker or one gene (haplotype approach) at a time. These ...

One problematic feature of Hall algebras is the fact that the standard multiplication and comultiplication maps do not satisfy the bialgebra compatibility condition in the underlying symmetric monoidal category Vect. In the past this problem has been resolved by working with a weaker structure called a ‘twisted’ bialgebra. In this paper we solve the problem differently by first switching to a d...