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Ralle
Ralle
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Is anyevery graded hereditary ring hereditary?

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Ralle
Ralle
  • 491
  • 2
  • 11

Let R be a graded (associative, unital) ring. If R is left graded hereditary (i.e. its left graded global dimension is 0 or 1), does it follow that R is left hereditary (i.e. its left global dimension is 0 or 1)?

Let R be a graded (associative, unital) ring. If R is left graded hereditary (i.e. its left graded global dimension is 0 or 1), does it follow that R is hereditary (i.e. its left global dimension is 0 or 1)?

Let R be a graded (associative, unital) ring. If R is left graded hereditary (i.e. its left graded global dimension is 0 or 1), does it follow that R is left hereditary (i.e. its left global dimension is 0 or 1)?

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Ralle
Ralle
  • 491
  • 2
  • 11

Is any graded hereditary ring hereditary?

Let R be a graded (associative, unital) ring. If R is left graded hereditary (i.e. its left graded global dimension is 0 or 1), does it follow that R is hereditary (i.e. its left global dimension is 0 or 1)?