noun which may take the genitive case particle 'no'
graded
Mathematical term used to describe algebraic structures (rings, modules, algebras) that are decomposed into a direct sum of pieces indexed by integers, often with a compatibility condition on multiplication. Common in phrases like 次数付き環 (graded ring) or 次数付き加群 (graded module).
多項式環は次数付き環の典型的な例である。
The polynomial ring is a typical example of a graded ring.
この定理は次数
This theorem holds for graded modules.
付き is a suffix meaning 'attached' or 'with'; here it forms a compound meaning 'equipped with a grading'.
Compound of 次数 (degree) + 付き (attached, with). The term is a direct translation of the English mathematical term 'graded'.