Principally Weakly and Weakly Coherent Monoids

Sedaghatjoo, Mojtaba; Khosravi, Roghaieh; Ershad, M.

doi:10.1080/00927870902828967

Cited by 13 publications

(6 citation statements)

References 6 publications

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“…There have been published several works on preservation of acts properties under products, for instance [2,3,4,5,9]. In this section we investigate another version of the problem for indecomposability property.…”

Section: Products Of Indecomposable Actsmentioning

confidence: 99%

Monoids over which products of indecomposable acts are indecomposable

Sedaghatjoo¹,

Khaksari²

2016

HJMS

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Section: Products Of Indecomposable Actsmentioning

confidence: 99%

Monoids over which products of indecomposable acts are indecomposable

Sedaghatjoo¹,

Khaksari²

2016

HJMS

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“…The converse of part (4) of Theorem 2.2 is not true. Consider the monoid S of Example 1.6 of [23]. S is left PSF and so S S satisfies Condition (P W P ssc ), by part (4) of Theorem 2.2, while S I S is not principally weakly flat, by [23,Proposition 1.5], and so it does not satisfy Condition (P W P ssc ), by part (1) of Theorem 2.8.…”

Section: Recall That For Any Nonempty Set I S Imentioning

confidence: 99%

“…Now, in the following example, we show that Condition (P W P ssc ) does not imply Condition (P W P E ) and so does not imply Condition (P W P ). In this example we use the monoid S of Example 1.6 of [23].…”

Section: Recall That For Any Nonempty Set I S Imentioning

confidence: 99%

Classification of monoids by Condition $(PWP_{ssc})$

Khamechi

Baluchestan

Saany

et al. 2020

CGASA

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Condition (P W P) which was introduced by Laan is related to the concept of flatness of acts over monoids. Golchin and Mohammadzadeh introduced Condition (P W PE) as a generalization of Condition (P W P). In this paper, we introduce Condition (P W Pssc) which is much easier to check than Conditions (P W P) and (P W PE) and does not imply them. Also principally weakly flat is a generalization of this condition. At first, general properties of Condition (P W Pssc) will be given. Finally a classification of monoids will be given for which all (cyclic, monocyclic) acts satisfy Condition (P W Pssc) and also a classification of monoids S will be given for which all right S-acts satisfying some other flatness properties have Condition (P W Pssc).

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“…Flatness properties of product acts over a monoid have been extensively studied in recent decades, see [9][10][11]. However, the research on flatness properties of product S -posets over a pomonoid S is so far less advanced.…”

Section: Introductionmentioning

confidence: 99%

On homological classification of pomonoids by GP-po-flatness of S-posets

2016

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Abstract:In this paper, we introduce GP-po-flatness property of S -posets over a pomonoid S , which lies strictly between principal weak po-flatness and po-torsion freeness. Furthermore, we investigate the homological classification problems of pomonoids by using this new property. Finally, we consider direct products of GP-po-flat S-posets. As an application, characterizations of pomonoids over which direct products of nonempty families of principally weakly po-flat S-posets are principally weakly po-flat are obtained, and some results of Khosravi, R. in a certain extent are generalized.

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Principally Weakly and Weakly Coherent Monoids

Cited by 13 publications

References 6 publications

Monoids over which products of indecomposable acts are indecomposable

Monoids over which products of indecomposable acts are indecomposable

Classification of monoids by Condition $(PWP_{ssc})$

On homological classification of pomonoids by GP-po-flatness of S-posets

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