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For a path algebra over a noetherian local ground ring, the notion of anadmissible ideal was defined by Raggi-C{\'a}rdenas and Salmer{\'o}n. We providesufficient conditions for admissibility and use them to study semiperfectmodule-finite algebras over local rings whose quotient by the radical is aproduct of copies of the residue field. We define string algebras over localground rings and recover the notion introduced by Butler and Ringel when theground ring is a field. We prove they are biserial in a sense of Kiri\v{c}enkoand Kostyukevich. We describe the syzygies of uniserial summands of theradical. We give examples of B\"{a}ckstr\"{o}m orders that are string algebrasover discrete valuation rings.

String algebras over local rings: admissibility and biseriality