• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.949-957
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• 1997

The purpose of this paper is to establish connection between certain complex of modules of generalized fractions and the concept of cosequence in commutative algebra. The main theorem of the paper leads to characterization, in terms of modules of generalized fractions, of regular (co) sequences.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.887-898
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• 2011

In this paper, we first discuss the convergence of the continued fractions of generalized Rogers-Ramanujan type in the modified sense. Then we prove several equalities concerning these continued fractions. The proofs of our main results are mainly based on the Bauer-Muir transformation.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.69-75
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• 1997

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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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.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.209-217
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• 1993

The multicollinearity problem in a multiple linear regression model may present deleterious effects on predictions. Thus, its is desirable to consider the optimal fractions with respect to the unbiased estimate of the mean squares errors of the predicted values. Interstingly, the optimal fractions can be also illuminated by the Bayesian inerpretation of the general James-Stein estimators.