Generalizations of decomposition theorems known over perfect rings

Mohamed, Saad H.; Singh, Surjeet

doi:10.1017/s144678870002084x

Cited by 21 publications

(23 citation statements)

References 11 publications

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“…(1)(2)(3)(4)(5)(6), Corollary 3.11) that an indecomposable d-continuous module has local endomorphism ring. These properties of an indecomposable d-continuous module will be used often in this paper without further reference.…”

Section: Introductionmentioning

confidence: 99%

Direct sums of dual continuous modules

Mohamed

Müller

1981

Math Z

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Section: Introductionmentioning

confidence: 99%

Direct sums of dual continuous modules

Mohamed

Müller

1981

Math Z

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“…Therefore these results hold for ^-continuous modules. In particular Proposition 3.7, Corollary 3.9, Proposition 4.1 and Corollary 4.2 in [13] give respectively the following four results. PROPOSITION [7]), and every d-complement submodule of M is a summand.…”

Section: Any Summand Of a Module M Satisfying Any Condition (D) Alsomentioning

confidence: 82%

“…It is obvious that Lemma 3.6 in [13] also holds for ^-continuous modules. Then a number of results were proved using only condition (D x ) and Lemma 3.6.…”

Section: Any Summand Of a Module M Satisfying Any Condition (D) Alsomentioning

confidence: 94%

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Quasi-dual-continuous modules

Mohamed

Müller

Singh³

1985

J Aust Math Soc A

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Quasi-dual-continuous modules, which generalize the concept of dual-continuous modules, are studied Mohamed, Muller and Singh had obtained some decomposition theorems and their partial canvwsfts, for dual-continuous modules. It is shown that these results can be extended to quasi-dual-continuous modules. Further, a short proof of a decomposition theorem for quasi-dual-continuous modules established recently by Oshiro is given. Some more structure theorems for such modules are established. Finally, quasi-dual-continuous covers are studied, and duals for results of Muller and Rizvi are derived.

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“…The following results about d-continuous modules are given in Mohamed and Singh (1977) and are listed here for easy reference. …”

Section: Some General Resultsmentioning

confidence: 99%

Rings with dual continuous right ideals

Mohamed

1982

J Aust Math Soc A

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In this paper the structure of rings with dual continuous right ideals is discussed. The main result is the following: If R is a ring with (Jacobson) radical nil, and all of its finitely generated right ideals are dual continuous, then R -(Q J) where S is a finite direct sum of local rings each of which has its radical square zero, or is a right valuation ring, 7* is semiprimary right semihereditary ring, and M is an (5, r)-bimodule such that all of its finitely generated 7"-submodules are projective. A partial converse of this result is obtained: any matrix ring of the above type with M = 0 has all of its finitely generated right ideals dual continuous.

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Generalizations of decomposition theorems known over perfect rings

Cited by 21 publications

References 11 publications

Direct sums of dual continuous modules

Direct sums of dual continuous modules

Quasi-dual-continuous modules

Rings with dual continuous right ideals

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