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Please solve this question .I hope its name is $1-$Tertiary amino cyclopentanone. But it have some mistakes.

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Cyclic amides of amino carboxylic acids are called lactams.

According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), lactames can be named by two methods:

P-66.1.5.1 Lactams and lactims

Intramolecular amides of amino carboxylic acids, $\ce{-CO-NH-{}}$, are called ‘lactams’ and their tautomers, $\ce{-C(OH)=N-{}}$, are ‘lactims’. Lactams are named in two ways:

(1) as heterocyclic pseudo ketones;

(2) by substituting ‘lactam’ for the ‘ic acid’ ending of a systematic ‘oic acid’ name for the parent acid without the amino substituent, and inserting a locant designating the position of the amino group between the ‘o’ and ‘lactam’. Lactims are named in the same way, using ‘lactim’ in place of ‘lactam’.

Method (1) generates preferred IUPAC names.

The corresponding heterocyclic parent structure is piperidine.

piperidine

Thus, the preferred IUPAC name for the lactam according to Method (1) is the pseudo ketone piperidin-2-one.

piperidin-2-one

The systematic name of the parent acid without the amino substituent is pentanoic acid.

pentanoic acid

Therefore, the lactam can also be named as pentano-5-lactam in accordance with Method (2).

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