Balmer spectrum of tensor $ n $-angulated categories

Lingling Tan; Lingling Tan

doi:10.3934/math.2026747

AIMS Mathematics

2026, Volume 11, Issue 6: 18402-18414. doi: 10.3934/math.2026747

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Balmer spectrum of tensor $ n $-angulated categories

Lingling Tan ^,

School of Artificial Intelligence, Jianghan University, Wuhan 430056, China

Received: 01 April 2026 Revised: 28 May 2026 Accepted: 12 June 2026 Published: 22 June 2026
MSC : 18F30, 18G25, 18G80

In this paper, we first introduce the notions of thick and prime tensor ideals in tensor $ n $-angulated categories and then obtain the Balmer spectrum of such categories. We consider the topological properties of this spectrum. Moreover, we introduce the notion of radical tensor ideals in tensor $ n $-angulated categories and show that they can be parametrized by supports of subcategories. Furthermore, we provide Balmer's classification theorem in terms of Thomason subsets of the spectrum space.
- tensor $ n $-angulated category,
- Balmer spectrum,
- thick,
- radical,
- Thomason subset
Citation: Lingling Tan. Balmer spectrum of tensor $ n $-angulated categories[J]. AIMS Mathematics, 2026, 11(6): 18402-18414. doi: 10.3934/math.2026747

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Abstract

In this paper, we first introduce the notions of thick and prime tensor ideals in tensor $ n $-angulated categories and then obtain the Balmer spectrum of such categories. We consider the topological properties of this spectrum. Moreover, we introduce the notion of radical tensor ideals in tensor $ n $-angulated categories and show that they can be parametrized by supports of subcategories. Furthermore, we provide Balmer's classification theorem in terms of Thomason subsets of the spectrum space.

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