… the endomorphism ring E = EndkG(M2n+1) is a local ring, then by [10] Proposition 6.10, M2n+1
is indecomposable kG-module. … Suppose P is a prime ideal of R containing integer p, and …

: The aim of this article is to summarize the relationship between double Ore extensions and
iterated Ore extensions, and mainly describe the lifting of properties from an algebra A to a (…

… The rank of a free module over a commutative ring is defined as the cardinality of a basis.
Now, … Zp is a principal ideal domain. It is clear that {xi} is an independent subset of OH over Zp. …

… ring ( [60] §10.4) with prime ideal p, perfect residue field κ and field of fractions F. We fix a
prime … [45] as an algebra of endomorphisms on finite dimensional spaces of modular forms (…

… Since B⊗R S is locally free over B, for s ∈ B⊗R S, the determinant of the endomorphism …
Let x = m ⊂ O be a prime ideal of residual characteristic ̸= p. Then Proposition 2.2 says fx is …

… abelian surfaces with endomorphism algebra equal to a matrix algebra of degree 2 over an
… In the case that R is a principal ideal domain, we identify the ideal DB with its generator, up …