循环表现模、投射覆盖与因子分解
Cyclically presented modules, projective covers and factorizations
摘要：
我们研究了循环表示模的投射覆盖，将其上每个循环表示模都有投射覆盖的环刻画为冯诺依曼正则模其Jacobson根$J(R)$且幂等元可以模$J(R)$提升的环$R$.循环表示模自然地出现在研究非必要交换整环中元素的因式分解中。可能的应用之一是模$M_R$，其自同态环$E:=(M_R)$是Von Neumann正则模$J(E)$，其中幂等元提升模$J(E)$。
英文摘要：
We investigate projective covers of cyclically presented modules, characterizing the rings over which every cyclically presented module has a projective cover as the rings $R$ that are Von Neumann regular modulo their Jacobson radical $J(R)$ and in which idempotents can be lifted modulo $J(R)$. Cyclically presented modules naturally appear in the study of factorizations of elements in non-necessarily commutative integral domains. One of the possible applications is to the modules $M_R$ whose endomorphism ring $E:=(M_R)$ is Von Neumann regular modulo $J(E)$ and in which idempotents lift modulo $J(E)$.
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