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Goodwill and Other Intangible Assets
 12 Months Ended
Dec. 31, 2019
Goodwill and Intangible Assets Disclosure [Abstract]  
Goodwill and Intangible Assets Disclosure GOODWILL AND OTHER INTANGIBLE ASSETS
The following table shows the changes in the carrying amount of goodwill for the years ended December 31:
 
2019
 
2018
Balance at beginning of year
$
534,780

 
$
539,838

Goodwill acquired
—

 
558

Foreign currency translation
1,199

 
(5,616
)
Balance at year end
$
535,979

 
$
534,780


Goodwill and indefinite-lived assets are reviewed for impairment on an annual basis in the fourth quarter. The Company completed its impairment review and determined that there had been no impairment of these assets through December 31, 2019. The Company identified no triggering events or other circumstances which indicated the carrying amount of goodwill or intangible assets may not be recoverable.
The components of other intangible assets as of December 31 are as follows:
 
2019
 
2018
 
Gross
Amount
 
Accumulated
Amortization
 
Intangibles, Net
 
Gross
Amount
 
Accumulated
Amortization
 
Intangibles, Net
Customer relationships
$
197,764

 
$
(58,851
)
 
$
138,913

 
$
197,942

 
$
(49,887
)
 
$
148,055

Proven technology and patents
75,170

 
(46,532
)
 
28,638

 
73,880

 
(42,750
)
 
31,130

Tradenames (finite life)
4,594

 
(3,124
)
 
1,470

 
4,504

 
(2,874
)
 
1,630

Tradenames (indefinite life)
35,474

 
—

 
35,474

 
35,500

 
—

 
35,500

Other
5,462

 
(3,715
)
 
1,747

 
3,684

 
(2,691
)
 
993

 
$
318,464

 
$
(112,222
)
 
$
206,242

 
$
315,510

 
$
(98,202
)
 
$
217,308


The Company recognized amortization expense associated with the above intangible assets of $15.1 million, $14.3 million, and $11.5 million for the years ended December 31, 2019, 2018, and 2017, respectively. The annual aggregate amortization expense based on the current balance of other intangible assets is estimated at $15.5 million for 2020, $14.3 million for 2021, $12.8 million for 2022, $13.5 million for 2023, and $11.8 million for 2024. The finite-lived intangible assets are amortized on a straight-line basis over periods ranging from 3 to 45 years. The straight-line method of amortization reflects an appropriate allocation of the cost of the intangible assets to earnings in proportion to the amount of economic benefits obtained by the Company in each reporting period. Purchased intangibles amortization was $14.3 million, $10.8 million after tax, $13.3 million, $10.0 million after tax, and $10.9 million, $7.1 million after tax, for the years ended December 31, 2019, 2018, and 2017, respectively.
In addition to the above amortization, the Company recorded amortization expense associated with capitalized software, which is included in Property, Plant and Equipment in Note 8, of $34.4 million, $33.0 million, and $31.0 million for the years ended December 31, 2019, 2018, and 2017, respectively.