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Goodwill and Other Intangible Assets
 12 Months Ended
Dec. 31, 2020
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:
20202019
Balance at beginning of year$535,979 $534,780 
Goodwill acquired6,169 — 
Foreign currency translation8,122 1,199 
Balance at year end$550,270 $535,979 
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, 2020. 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:
 20202019
Gross
Amount		Accumulated
Amortization		Intangibles, NetGross
Amount		Accumulated
Amortization		Intangibles, Net
Customer relationships$201,445 $(68,319)$133,126 $197,764 $(58,851)$138,913 
Proven technology and patents78,312 (52,138)26,174 75,170 (46,532)28,638 
Tradenames (finite life)4,896 (3,444)1,452 4,594 (3,124)1,470 
Tradenames (indefinite life)35,595 — 35,595 35,474 — 35,474 
Other5,215 (4,777)438 5,462 (3,715)1,747 
 $325,463 $(128,678)$196,785 $318,464 $(112,222)$206,242 

The Company recognized amortization expense associated with the above intangible assets of $15.7 million, $15.1 million, and $14.3 million for the years ended December 31, 2020, 2019, and 2018, respectively. The annual aggregate amortization expense based on the current balance of other intangible assets is estimated at $14.7 million for 2021, $13.2 million for 2022, $13.5 million for 2023, $12.9 million for 2024, and $11.8 million for 2025. 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 $14.9 million, $11.2 million after tax, $14.3 million, $10.8 million after tax, and $13.3 million, $10.0 million after tax, for the years ended December 31, 2020, 2019, and 2018, 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 $40.7 million, $34.4 million, and $33.0 million for the years ended December 31, 2020, 2019, and 2018, respectively.