Componentwise injective models of functors to DGAs
The aim of this paper is to present a starting point for proving existence of injective minimal models (cf. [8]) for some systems of complete differential graded algebras.
The aim of this paper is to present a starting point for proving existence of injective minimal models (cf. [8]) for some systems of complete differential graded algebras.
We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra , the Verma module over a Kac-Moody algebra, the Verma module...
First, we give complete description of the comultiplication modules over a Dedekind domain. Second, if is the pullback of two local Dedekind domains, then we classify all indecomposable comultiplication -modules and establish a connection between the comultiplication modules and the pure-injective modules over such domains.