INTEGRAL DOMAINS OF FINITE t-CHARACTER Introduction An
... if every nonzero nonunit of D belongs to at most a finite number of maximal ideals (resp., maximal t-ideals). It is well known that integral domains in which each tideal is a v-ideal (e.g., Noetherian, Mori, or Krull domains) are of finite t-character [26, Theorem 1.3]. Also, if D is of finite t-cha ...
... if every nonzero nonunit of D belongs to at most a finite number of maximal ideals (resp., maximal t-ideals). It is well known that integral domains in which each tideal is a v-ideal (e.g., Noetherian, Mori, or Krull domains) are of finite t-character [26, Theorem 1.3]. Also, if D is of finite t-cha ...
![STRONGLY PRIME GROUP RINGS 1. Introduction ([8], Conjecture](http://s1.studyres.com/store/data/019252257_1-b8d019fa7c7ba8d94ef2c727e781bf62-300x300.png)
The ring of formal power series
... metric. This automatically gives R[[X]] the structure of a topological ring (and even of a complete metric space). But the general construction of a completion of a metric space is more involved than what is needed here, and would make formal power series seem more complicated than they are. It is p ...
... metric. This automatically gives R[[X]] the structure of a topological ring (and even of a complete metric space). But the general construction of a completion of a metric space is more involved than what is needed here, and would make formal power series seem more complicated than they are. It is p ...
A Relative Spectral Sequence for Topological Hochschild Homology
... commutative S-algebra, and M and N are R-algebras. Recall that if k is an S-algebra, an k-algebra R is called q-cofibrant if the unit map k → R is a cofibration in the Quillen model category of kalgebras (see section VII.4 of [EKMM]); similarly R is called a q-cofibrant commutative k-algebra if its ...
... commutative S-algebra, and M and N are R-algebras. Recall that if k is an S-algebra, an k-algebra R is called q-cofibrant if the unit map k → R is a cofibration in the Quillen model category of kalgebras (see section VII.4 of [EKMM]); similarly R is called a q-cofibrant commutative k-algebra if its ...
a basis for free lie rings and higher commutators in free groups
... by an associative ring using the rule (2.2). In particular [l, Theorem 3], the free Lie ring generated by xi, ■ • ■ , xq is faithfully represented by the free associative ring generated by In the free associative ring a monomial is determined by the order of its factors, since all possible ways of i ...
... by an associative ring using the rule (2.2). In particular [l, Theorem 3], the free Lie ring generated by xi, ■ • ■ , xq is faithfully represented by the free associative ring generated by In the free associative ring a monomial is determined by the order of its factors, since all possible ways of i ...
Lectures on Modules over Principal Ideal Domains
... 4. Consider R as a module over itself. Prove that a singleton set {x} is linearly independent if and only if x is not a zero divisor in R. 5. State and prove the fundamental homomorphism theorems for modules. We shall now illustrate several basic results on vector spaces that fail for modules over c ...
... 4. Consider R as a module over itself. Prove that a singleton set {x} is linearly independent if and only if x is not a zero divisor in R. 5. State and prove the fundamental homomorphism theorems for modules. We shall now illustrate several basic results on vector spaces that fail for modules over c ...
SERRE DUALITY FOR NONCOMMUTATIVE PROJECTIVE
... the shift operator. If proj A has a dualizing sheaf ω 0 , then, for each i, there is a natural transformation θi : Extiqgr A (−, ω 0 ) −→ Hd−i (X, −)∗ . Under some hypotheses Theorem 2.3 gives a sufficient and necessary condition for a dualizing sheaf to exist. Namely, to show the existence of a dua ...
... the shift operator. If proj A has a dualizing sheaf ω 0 , then, for each i, there is a natural transformation θi : Extiqgr A (−, ω 0 ) −→ Hd−i (X, −)∗ . Under some hypotheses Theorem 2.3 gives a sufficient and necessary condition for a dualizing sheaf to exist. Namely, to show the existence of a dua ...