The Category of S-Posets

Bulman-Fleming, Sydney; Mahmoudi, Mojgan

doi:10.1007/s00233-005-0540-y

Cited by 69 publications

(63 citation statements)

References 7 publications

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“…The following proposition shows that right S -posets satisfying Condition (P W P ) w are closed under directed colimits. For more information about directed colimits in the category P OS -S the reader is referred to [2,3].…”

Section: S -Posets Satisfying Condition (P W P ) Wmentioning

confidence: 99%

“…Proof Let (A i , ϕ i,j ) be a direct system of right S -posets satisfying Condition (P W P ) w over a directed index first appeared in [3].…”

Section: Proposition 22 Every Directed Colimit Of a Direct System Ofmentioning

confidence: 99%

“…For S -posets, the definition of the S -poset A(I) was introduced in [3]. Qiao et al in [9] proved that A(I) fails to satisfy Condition (P ).…”

Section: Introductionmentioning

confidence: 99%

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On Condition $(PWP)_{w}$ for $S$-posets

Liang¹,

Luo²

2015

Turk J Math

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In this paper, we continue to study this condition. We first present a necessary and sufficient condition under which the S -poset A(I) satisfies Condition (P W P )w . Furthermore, we characterize pomonoids S over which all cyclic (Rees factor) S -posets satisfy Condition (P W P )w , and pomonoids S over which all Rees factor S -posets satisfying Condition (P W P )w have a certain property. Finally, we consider direct products of S -posets satisfying Condition (P W P )w .

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Section: S -Posets Satisfying Condition (P W P ) Wmentioning

confidence: 99%

“…Proof Let (A i , ϕ i,j ) be a direct system of right S -posets satisfying Condition (P W P ) w over a directed index first appeared in [3].…”

Section: Proposition 22 Every Directed Colimit Of a Direct System Ofmentioning

confidence: 99%

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On Condition $(PWP)_{w}$ for $S$-posets

Liang¹,

Luo²

2015

Turk J Math

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“…For more information about dcpos we refer to [1,7], about S-sets see [5,9], about S-posets see [3], and for S-dcpos refer to [11,12].…”

Section: Introductionmentioning

confidence: 99%

Weighted limits in the category Dcpo-S

Farsad¹,

Halimeh

2016

Asian-European J. Math.

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“…The class of left S-posets and S-morphisms forms a category, which we denote by S-Pos (see [2]). In S-Pos, one should note that an S-isomorphism f : A → C is an order-and action-preserving bijection and f −1 : C → A is also a monotonic map.…”

mentioning

confidence: 99%

Ordered left PP monoids

Shi

2014

Mathematica Slovaca

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ABSTRACT. An ordered monoid S in which every principal left ideal, regarded as an S-poset, is projective is called an ordered left P P monoid, for short, an ordered lpp monoid. In this paper, we introduce a new kind of ordered relations instead of Green relations adopted by J. B. Fountain, ordered lpp monoids are described by these ordered relations. Some similar results of c-rpp semigroups are duduced and proved, in particular, Fountain's results about C-lpp monoids are generalized to ordered monoids.

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The Category of S-Posets

Cited by 69 publications

References 7 publications

On Condition $(PWP)_{w}$ for $S$-posets

On Condition $(PWP)_{w}$ for $S$-posets

Weighted limits in the category Dcpo-S

Ordered left PP monoids

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