On pure Goldie dimensions

ABSTRACT

In this paper, we examine the pure Goldie dimension and dual pure Goldie dimension in finitely accessible additive categories. In particular, we show that if A is an object in a finitely accessible additive category 𝒜 that has finite pure Goldie dimension n and finite dual pure Goldie dimension m, then End_𝒜(A) is semilocal and the dual Goldie dimension of End_𝒜(A) is less than or equal to n+m.

KEYWORDS:

• Accessible categories
• Camps–Dicks theorem
• dual pure Goldie dimension
• pure Goldie dimension

MATHEMATICS SUBJECT CLASSIFICATION:

• 18C35
• 18A25
• 16D70
• 16G10