Indecomposable modules for the dual immaculate basis of quasi-symmetric functions

The immaculate basis of the non - commutative symmetric functions ( Extended Abstract )

We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions and decompose Schur functions according to a signed combinatorial formula. Résumé. Nous introduisons une nouvelle base des fonctions symé...

Multiplicative structures of the immaculate basis of non-commutative symmetric functions

Gröbner Basis and Indecomposable Modules over a like Dedekind Ring

Using Gröbner Basis, we introduce a general algorithm to determine the additive structure of a module, when we know about it using indirect information about its structure. We apply the algorithm to determine the additive structure of indecomposable modules over ZCp, where Cp is the cyclic group of order a prime number p, and the p−pullback {Z→ Zp ← Z} of Z⊕Z.

Dual bases for non commutative symmetric and quasi-symmetric functions via monoidal factorization

where O(P ) is the (multi-)set of roots of P (a polynomial) invites to consider Λj(?) as a “multiset (endo)functor” rather than a function K → K (K is a field where P splits). But, here, Λk(X) = 0 whenever |X | < k and one would like to get the universal formulas i.e. which hold true whatever the cardinality of |X |. This set of formulas is obtained as soon as the alphabet is infinite and, ther...

Absolutely Indecomposable Modules

A module is called absolutely indecomposable if it is directly indecomposable in every generic extension of the universe. We want to show the existence of large abelian groups that are absolutely indecomposable. This will follow from a more general result about R-modules over a large class of commutative rings R with endomorphism ring R which remains the same when passing to a generic extension...