Subjects: Mathematics >> Algebra and Number Theory submitted time 2023-12-11
Abstract: Let be a k-algebra defined over a field k. This paper consider the two questions: If the tensor M⊗N on A is zero, under what situation is either M = 0 or N = 0? If the element, say m⊗n , in M⊗N is zero, under what situation is either m=0 or n = 0?
Subjects: Mathematics >> Algebra and Number Theory Subjects: Mathematics >> Discrete Mathematics and Combinatorics submitted time 2023-12-04
Abstract: Let $A_n$ be the Nakayama algebra of type $A$ with quadratic Jacobson radical to be zero and $X_n$ be the Nakayama algebra of type $A$ with quadratic Jacobson radical to be zero. In this paper, we consider the k-tensor $A_n otimes X_n$ and the classification of the indecomposable modules over $A_n otimes X_n$. Moreover, we provide a counting formula to compute the number of isoclasses of indecomposable $A_n otimes X_n$ -modules.
Peer Review Status:Awaiting Review