Bulletin of the Iranian Mathematical Society, 2020
We study the class of one-dimensional Cohen-Macaulay local rings with canonical reductions, i.e.,... more We study the class of one-dimensional Cohen-Macaulay local rings with canonical reductions, i.e., admit canonical ideals which are reductions of the maximal ideals, show that it contains the class of almost Gorenstein rings, and study characterizations for rings obtained by idealizations or by numerical semigroup rings to have canonical reductions. Keywords Cohen-Macaulay local ring • Gorenstein ring • Almost Gorenstein ring • Canonical ideal • Canonical reduction Mathematics Subject Classification 13H10 • 13H15 dim(M) R (R/m, M)). If I and J are two proper ideals of R, such that J ⊆ I , then J is said to be a reduction of I if I n+1 = J I n for all n 0. We set red I (J) = min{n ∈ N | I n+1 = J I n } Communicated by Rahim Zaare-Nahandi.
Let A be a Cohen-Macaulay local ring with dim A = d ≥ 3, possessing the canonical module K A. Let... more Let A be a Cohen-Macaulay local ring with dim A = d ≥ 3, possessing the canonical module K A. Let a 1 , a 2 ,. .. , a r (3 ≤ r ≤ d) be a subsystem of parameters of A and set Q = (a 1 , a 2 ,. .. , a r). It is shown that if the Rees algebra R(Q) of Q is an almost Gorenstein graded ring, then A is a regular local ring and a 1 , a 2 ,. .. , a r is a part of a regular system of parameters of A.
The aim of this note is to study the class of one dimensional Cohen-Macaulay local rings, $(R, \f... more The aim of this note is to study the class of one dimensional Cohen-Macaulay local rings, $(R, \fm)$ say, possessing a canonical ideal $K$ which is a reduction of $\fm$. We call $R$ to have canonical reduction $K$. We show that the class of rings with canonical reductions contains the class of almost Gorenstein rings and establish its relation with rings obtained by idealizations and also with numerical semigroup rings.
Bulletin of the Iranian Mathematical Society, 2020
We study the class of one-dimensional Cohen-Macaulay local rings with canonical reductions, i.e.,... more We study the class of one-dimensional Cohen-Macaulay local rings with canonical reductions, i.e., admit canonical ideals which are reductions of the maximal ideals, show that it contains the class of almost Gorenstein rings, and study characterizations for rings obtained by idealizations or by numerical semigroup rings to have canonical reductions. Keywords Cohen-Macaulay local ring • Gorenstein ring • Almost Gorenstein ring • Canonical ideal • Canonical reduction Mathematics Subject Classification 13H10 • 13H15 dim(M) R (R/m, M)). If I and J are two proper ideals of R, such that J ⊆ I , then J is said to be a reduction of I if I n+1 = J I n for all n 0. We set red I (J) = min{n ∈ N | I n+1 = J I n } Communicated by Rahim Zaare-Nahandi.
Let A be a Cohen-Macaulay local ring with dim A = d ≥ 3, possessing the canonical module K A. Let... more Let A be a Cohen-Macaulay local ring with dim A = d ≥ 3, possessing the canonical module K A. Let a 1 , a 2 ,. .. , a r (3 ≤ r ≤ d) be a subsystem of parameters of A and set Q = (a 1 , a 2 ,. .. , a r). It is shown that if the Rees algebra R(Q) of Q is an almost Gorenstein graded ring, then A is a regular local ring and a 1 , a 2 ,. .. , a r is a part of a regular system of parameters of A.
The aim of this note is to study the class of one dimensional Cohen-Macaulay local rings, $(R, \f... more The aim of this note is to study the class of one dimensional Cohen-Macaulay local rings, $(R, \fm)$ say, possessing a canonical ideal $K$ which is a reduction of $\fm$. We call $R$ to have canonical reduction $K$. We show that the class of rings with canonical reductions contains the class of almost Gorenstein rings and establish its relation with rings obtained by idealizations and also with numerical semigroup rings.
Uploads
Papers by Mehran Rahimi