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• # Artykuł - szczegóły

## Open Mathematics

2006 | 4 | 2 | 250-259

## Squared cycles in monomial relations algebras

EN

### Abstrakty

EN
Let $$\mathbb{K}$$ be an algebraically closed field. Consider a finite dimensional monomial relations algebra $$\Lambda = {{\mathbb{K}\Gamma } \mathord{\left/ {\vphantom {{\mathbb{K}\Gamma } I}} \right. \kern-\nulldelimiterspace} I}$$ of finite global dimension, where Γ is a quiver and I an admissible ideal generated by a set of paths from the path algebra $$\mathbb{K}\Gamma$$ . There are many modules over Λ which may be represented graphically by a tree with respect to a top element, of which the indecomposable projectives are the most natural example. These trees possess branches which correspond to right subpaths of cycles in the quiver. A pattern in the syzygies of a specific factor module of the corresponding indecomposable projective module is found, allowing us to conclude that the square of any cycle must lie in the ideal I.

EN

250-259

wydano
2006-06-01
online
2006-06-01

### Twórcy

autor
• California State University, Stanislaus

### Bibliografia

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