An automated bolus-tracking program can be used to optimize the timing of hepatic arterial phase CT. Multiphasic CT performed using this technique is useful in detection of small hepatocellular carcinoma.
Let O be a complete discrete valuation ring with unique maximal ideal ( ) and residue class field k = O/( ), and let be an O-order.¯ denotes the k-algebra / . In this paper, we study Heller lattices of¯ -modules and investigate sufficient conditions of their indecomposability (Theorem 2.9). Also, we show that some short exact sequences of¯ -modules are, modulo direct summands of split sequences, liftable to short exact sequences of -lattices (Theorem 3.2). In the final section, we shall apply our results on orders to the group ring = OG of a finite group G over O (Theorem 4.4).Let (K, ) ⊃ (K , ) be an extension of complete discrete valuation fields, and let O (resp. O ) be a valuation ring of (resp. ) with unique maximal ideal ( ) (resp. ( )) and the residue class field k = O/( ) (resp. k = O /( )). Then O ⊃ O is an extension of complete discrete valuation rings and ( ) = ( ) ∩ O . Also, we regard k = O /( )(O + ( ))/( ) as a subfield of k = O/( ). Let e be the ramification index of over , so e = v for some unit v in O. Throughout this paper, we assume that e 3, so ( 3 ) ⊇ ( ).Let G be a finite group and p a prime number dividing the order of G. Suppose that (K, O, k) is a p-modular system and P is an indecomposable projective module over the
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