• 충청수학회지
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• 제7권1호
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• pp.153-164
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• 1994

Let A be a commutative ring with identity and M an A-module. When $U_n$ is a triangular subset of $A_n$, Sharp and Zakeri defined a module of generalized fractions $U_n^{-n}M$. In [SZ3], they described a relation of the Monomial Conjecture and a module of generalized fractions under the condition of a Noetherian local ring. In this paper, we investigate some properties of non-zero generalized fractions and give a generalization of results of Sharp and Zakeri for an arbitrary ring.

• 대한수학회지
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• 제32권2호
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• pp.265-277
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• 1995

In [9], we gave a very explicit description of the injective envelope of an arbitray simple module over a polynomial ring $K[X_1, \ldots, X_n]$ over a field K in indeterminates $X_1, \ldots, X_n$. This paper presents another approach to give a description.

• 대한수학회지
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• 제33권4호
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• pp.747-761
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• 1996

Thoughout this paper, R will be a commutative ring (with non-zero identity) and M will denote an R-module.

• 대한수학회지
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• 제34권1호
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• pp.69-75
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• 1997

• 충청수학회지
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• 제9권1호
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• pp.17-25
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• 1996

We study the relationship between a property of a triangular subset and coassociated prime ideals of the module of generalized fractions induced by the triangular subset, and investigate coassociated prime ideals of modules of generalized fractions defined by some special triangular subsets.

• 대한수학회보
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• 제42권1호
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• pp.87-92
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• 2005

Let A be a polynomial ring over a field and M a simple A-module. We generalize one result of Song about the description of the injective envelope $E_A$ (M) in terms of modules of generalized fractions.

• 충청수학회지
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• 제9권1호
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• pp.61-68
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• 1996

We investigate associated prime ideals of the module of generalized fractions defined by poor essential sequences and extend the McAdam and Ratliff's criterion of locally unmixed rings.

• 대한수학회보
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• 제35권2호
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• pp.363-374
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• 1998

We investigate relationships of E-depths and T-codepths of modules in s short exact exact sequence. We give E-depths and T-codepths of some modules.