We first introduce the concepts of absolutely E-pure modules and E-pure split modules. Then, we characterize the IF rings in terms of absolutely E-pure modules. The E-pure split modules are also characterized.
In this paper we study the existence of FIn-envelopes, FI1/n-envelopes and FIn-covers, where FIn denotes the class of all n-absolute pure modules for an integer n 〉 0 or n = ∞. We prove that FI1/n-envelopes and FIn-...In this paper we study the existence of FIn-envelopes, FI1/n-envelopes and FIn-covers, where FIn denotes the class of all n-absolute pure modules for an integer n 〉 0 or n = ∞. We prove that FI1/n-envelopes and FIn-covers exist over an n-coherent ring R, and FIn-covers and special FIn-preenvelopes exist over any ring R.展开更多
文摘We first introduce the concepts of absolutely E-pure modules and E-pure split modules. Then, we characterize the IF rings in terms of absolutely E-pure modules. The E-pure split modules are also characterized.
文摘In this paper we study the existence of FIn-envelopes, FI1/n-envelopes and FIn-covers, where FIn denotes the class of all n-absolute pure modules for an integer n 〉 0 or n = ∞. We prove that FI1/n-envelopes and FIn-covers exist over an n-coherent ring R, and FIn-covers and special FIn-preenvelopes exist over any ring R.
