The goal of this paper is to investigate whether the Ext-groups of all pairs (M, N) of modules over Nakayama algebras of type (n,n,n) satisfy the condition ExtΛn(M,N)=0 for n >> 0 ? ExtΛn(M,N)=0 for n >>...The goal of this paper is to investigate whether the Ext-groups of all pairs (M, N) of modules over Nakayama algebras of type (n,n,n) satisfy the condition ExtΛn(M,N)=0 for n >> 0 ? ExtΛn(M,N)=0 for n >> 0. We achieve that by discussing the Ext-groups of Nakayama algebra with projectives of lengths 3n+1 and 3n+2 using combinations of modules of different lengths.展开更多
ring R is called right principally-injective if every R-homomorphism f:aR→R,a∈R,extends to R,or equivalently,if every system of equations xa=b(a,b∈R)is solvable in R.In this paper we show that for any arbitrary gra...ring R is called right principally-injective if every R-homomorphism f:aR→R,a∈R,extends to R,or equivalently,if every system of equations xa=b(a,b∈R)is solvable in R.In this paper we show that for any arbitrary graph E and for a field K,principally-injective conditions for the Leavitt path algebra LK(E)are equivalent to that graph E being acyclic.We also show that the principally-injective Leavitt path algebras are precisely the von Neumann regular Leavitt path algebras.展开更多
文摘The goal of this paper is to investigate whether the Ext-groups of all pairs (M, N) of modules over Nakayama algebras of type (n,n,n) satisfy the condition ExtΛn(M,N)=0 for n >> 0 ? ExtΛn(M,N)=0 for n >> 0. We achieve that by discussing the Ext-groups of Nakayama algebra with projectives of lengths 3n+1 and 3n+2 using combinations of modules of different lengths.
文摘ring R is called right principally-injective if every R-homomorphism f:aR→R,a∈R,extends to R,or equivalently,if every system of equations xa=b(a,b∈R)is solvable in R.In this paper we show that for any arbitrary graph E and for a field K,principally-injective conditions for the Leavitt path algebra LK(E)are equivalent to that graph E being acyclic.We also show that the principally-injective Leavitt path algebras are precisely the von Neumann regular Leavitt path algebras.
