Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Some infinitely generated non-projective modules over path algebras and their extensions under Martin's axiom
Ayako ItabaDiego A. MejíaTeruyuki Yorioka
著者情報
ジャーナル フリー

2020 年 72 巻 2 号 p. 413-433

詳細
抄録

In this paper it is proved that, when 𝑄 is a quiver that admits some closure, for any algebraically closed field 𝐾 and any finite dimensional 𝐾-linear representation 𝒳 of 𝑄, if Ext1𝐾𝑄(𝒳, 𝐾𝑄) = 0 then 𝒳 is projective. In contrast, we show that if 𝑄 is a specific quiver of the type above, then there is an infinitely generated non-projective 𝐾𝑄-module 𝑀𝜔_1 such that, when 𝐾 is a countable field, 𝐌𝐀ℵ_1 (Martin's axiom for ℵ1 many dense sets, which is a combinatorial axiom in set theory) implies that Ext1𝐾𝑄(𝑀𝜔_1, 𝐾𝑄) = 0.

著者関連情報

この記事は最新の被引用情報を取得できません。

© 2020 The Mathematical Society of Japan
前の記事 次の記事
feedback
Top