Flatness properties of acts over semigroups

Laan, Valdis; Reimaa, Ülo; Tart, Lauri; Teor, Elery

doi:10.52547/cgasa.15.1.59

Cited by 1 publication

(9 citation statements)

References 7 publications

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“…The first implication follows from Proposition 2.6 and Lemma 3.2. The second implication holds due to Proposition 4.3 in [15].…”

Section: Sequence Actsmentioning

confidence: 87%

“…It is easy to see that M S satisfies Condition (LC): if , then there exist and such that and . By Theorem 4.2 in [15], right sequence acts are finite limit flat. We also know that they are unitary.…”

Section: The Main Theoremmentioning

confidence: 98%

“…(7) (6). Every right sequence act M S satisfies Condition (E) by Lemma 3.10 in [15]. It is easy to see that M S satisfies Condition (LC): if , then there exist and such that and .…”

Section: The Main Theoremmentioning

confidence: 99%

“…Let us recall the construction of a sequence act over a semigroup (cf. [15, Construction 3.9]). A similar construction in the case of a monoid appeared already in the proof of Lemma 1 in [6].…”

Section: Sequence Actsmentioning

confidence: 99%

“…(7) (9). A finite limit flat act A S must satisfy Condition (LC) by Theorem 4.2 in [15]. This implies that A S is indecomposable.…”

Section: The Main Theoremmentioning

confidence: 99%

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Perfection for semigroups

Laan¹,

Lepik²

2023

Proceedings of the Edinburgh Mathematical Society

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We call a semigroup right perfect if every object in the category of unitary right acts over that semigroup has a projective cover. In this paper, we generalize results about right perfect monoids to the case of semigroups. In our main theorem, we will give nine conditions equivalent to right perfectness of a factorizable semigroup. We also prove that right perfectness is a Morita invariant for factorizable semigroups.

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“…The first implication follows from Proposition 2.6 and Lemma 3.2. The second implication holds due to Proposition 4.3 in [15].…”

Section: Sequence Actsmentioning

confidence: 87%

Section: The Main Theoremmentioning

confidence: 98%

“…(7) (6). Every right sequence act M S satisfies Condition (E) by Lemma 3.10 in [15]. It is easy to see that M S satisfies Condition (LC): if , then there exist and such that and .…”

Section: The Main Theoremmentioning

confidence: 99%

Section: Sequence Actsmentioning

confidence: 99%

“…(7) (9). A finite limit flat act A S must satisfy Condition (LC) by Theorem 4.2 in [15]. This implies that A S is indecomposable.…”

Section: The Main Theoremmentioning

confidence: 99%

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