Let R be a commutative ring with nonzero identity and n be a positive integer.In this paper,we introduce and investigate a new subclass ofϕ-n-absorbing primary ideals,which are calledϕ-(n,N)-ideals.Letϕ:I(R)→I(R)∪{∅...Let R be a commutative ring with nonzero identity and n be a positive integer.In this paper,we introduce and investigate a new subclass ofϕ-n-absorbing primary ideals,which are calledϕ-(n,N)-ideals.Letϕ:I(R)→I(R)∪{∅}be a function,where I(R)denotes the set of all ideals of R.A proper ideal I of R is called aϕ-(n,N)-ideal if x1⋯xn+1∈I\ϕ(R)and x1⋯xn∉I imply that the product of xn+1 with(n−1)of x1,…,xn is in 0–√for all x1,…,xn+1∈R.In addition to giving many properties ofϕ-(n,N)-ideals,we also use the concept ofϕ-(n,N)-ideals to characterize rings that have only finitely many minimal prime ideals.展开更多
There is a variety of nice results about strongly Gorenstein flat modules over coherent rings. These results are done by Ding, Lie and Mao. The aim of this paper is to generalize some of these results, and to give hom...There is a variety of nice results about strongly Gorenstein flat modules over coherent rings. These results are done by Ding, Lie and Mao. The aim of this paper is to generalize some of these results, and to give homological descriptions of the strongly Gorenstein flat dimension (of modules and rings) over arbitrary associative rings.展开更多
文摘Let R be a commutative ring with nonzero identity and n be a positive integer.In this paper,we introduce and investigate a new subclass ofϕ-n-absorbing primary ideals,which are calledϕ-(n,N)-ideals.Letϕ:I(R)→I(R)∪{∅}be a function,where I(R)denotes the set of all ideals of R.A proper ideal I of R is called aϕ-(n,N)-ideal if x1⋯xn+1∈I\ϕ(R)and x1⋯xn∉I imply that the product of xn+1 with(n−1)of x1,…,xn is in 0–√for all x1,…,xn+1∈R.In addition to giving many properties ofϕ-(n,N)-ideals,we also use the concept ofϕ-(n,N)-ideals to characterize rings that have only finitely many minimal prime ideals.
文摘There is a variety of nice results about strongly Gorenstein flat modules over coherent rings. These results are done by Ding, Lie and Mao. The aim of this paper is to generalize some of these results, and to give homological descriptions of the strongly Gorenstein flat dimension (of modules and rings) over arbitrary associative rings.
