AbstractLet V be an m-dimensional discrete valuation domain. It is known that the power series ring V〚x〛 has t-dimension m. We will show that V〚x1,…,xn〛 has t-dimension 2m−1 for all n⩾2
AbstractFor an integral domain D of dimension n, the dimension of the polynomial ring D[x] is known ...
AbstractWe show that a ring is a Krull ring if and only if every nonzero regular prime ideal contain...
summary:The paper studies the structure of the ring A of arithmetical functions, where the multiplic...
AbstractLet V be a valuation domain. It is known that V〚X1,…,Xn〛V−(0) is an n-dimensional Noetherian...
Let V be a one-dimensional nondiscrete valuation domain and let V* = V \ {0}. We prove that Krull-di...
AbstractLet V (resp. D) be a valuation domain (resp. SFT Prüfer domain), I a proper ideal, and V̂ (r...
A ring D is called an SFT ring if for each ideal I of D, there exist a finitely generated ideal J of...
AbstractLet k⊂K be fields, let k0 be the maximal separable extension of k in K, and let x1,…,xn be a...
AbstractLet V be a valuation domain. It is known that V〚X1,…,Xn〛V−(0) is an n-dimensional Noetherian...
AbstractLet R be a globalized pseudo-valuation domain (for short, GPVD) with Krull dimension n. It i...
AbstractLet D be an integral domain, X be an indeterminate over D, and D[[X]] be the power series ri...
AbstractLet D be a domain with quotient field K. For any non-zero x∈D, we consider the ring Bx(D)={f...
AbstractLet D be an integral domain, X be an indeterminate over D, and D[[X]] be the power series ri...
An ideal I of a commutative ring R with identity is called an SFT (strong finite type) ideal if ther...
AbstractAn ideal I is called an SFT-ideal if there exist a natural number n and a finitely generated...
AbstractFor an integral domain D of dimension n, the dimension of the polynomial ring D[x] is known ...
AbstractWe show that a ring is a Krull ring if and only if every nonzero regular prime ideal contain...
summary:The paper studies the structure of the ring A of arithmetical functions, where the multiplic...
AbstractLet V be a valuation domain. It is known that V〚X1,…,Xn〛V−(0) is an n-dimensional Noetherian...
Let V be a one-dimensional nondiscrete valuation domain and let V* = V \ {0}. We prove that Krull-di...
AbstractLet V (resp. D) be a valuation domain (resp. SFT Prüfer domain), I a proper ideal, and V̂ (r...
A ring D is called an SFT ring if for each ideal I of D, there exist a finitely generated ideal J of...
AbstractLet k⊂K be fields, let k0 be the maximal separable extension of k in K, and let x1,…,xn be a...
AbstractLet V be a valuation domain. It is known that V〚X1,…,Xn〛V−(0) is an n-dimensional Noetherian...
AbstractLet R be a globalized pseudo-valuation domain (for short, GPVD) with Krull dimension n. It i...
AbstractLet D be an integral domain, X be an indeterminate over D, and D[[X]] be the power series ri...
AbstractLet D be a domain with quotient field K. For any non-zero x∈D, we consider the ring Bx(D)={f...
AbstractLet D be an integral domain, X be an indeterminate over D, and D[[X]] be the power series ri...
An ideal I of a commutative ring R with identity is called an SFT (strong finite type) ideal if ther...
AbstractAn ideal I is called an SFT-ideal if there exist a natural number n and a finitely generated...
AbstractFor an integral domain D of dimension n, the dimension of the polynomial ring D[x] is known ...
AbstractWe show that a ring is a Krull ring if and only if every nonzero regular prime ideal contain...
summary:The paper studies the structure of the ring A of arithmetical functions, where the multiplic...
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